Was the twist for the 75th Hunger Games predetermined?

It is unknown whether Snow changed the plan for the third quarter quell to send Katniss back into the Games but it is likely that he did.

A great number of the games were planned at the outset of the creation of the Hunger Games, including the concept of the Quarter Quell having an extra twist, but there's no information, either in the films or in the books that definitively say whether what occurred in the 75th Hunger Games was the plan or whether Snow changed it.

Every 25 years there is a Quarter Quell edition of the Hunger Games. Quells mark the anniversaries of the districts' defeat by the Capitol, and include special celebrations. The Games involves some sort of twist that makes them even more disastrous or difficult to compete in, or watch. A small box contains small yellow envelopes containing specific themes or twists for each Quarter Quell. These instructions were planned at the founding of the Hunger Games, with plans in place for hundreds of Games. The President at the time selects the appropriate card and reads it on live television to announce the theme of that year's Quell. It is unknown how many Quarter Quells were planned ahead of time, but some suspect that the 75th had been changed so that Katniss Everdeen, the female tribute from District 12 who won the previous year and the district's sole living female Victor, would be forced to go back into the arena once more (this is confirmed in a deleted scene in the film adaption of The Hunger Games: Catching Fire).

One point made in the article argues that it's unlikely that it was planned from the beginning... there was no way the founders could predict that there would be appropriate candidates for the games if this were the case. Until Katniss won the 74th Games with Peeta, there was no living female Victor from District 12, and it's unknown whether there had ever been one at all:

The 75th Hunger Games had past victors from earlier Hunger Games compete for a second time. This action was made to destroy any bonds the districts had with each other and to make them feel weak. It was meant to be a reminder to the citizens of the districts that even the strongest among them cannot overcome the power of the Capitol. It is speculated that this twist was not planned at the founding of the Hunger Games, but was designed specifically to force Katniss back into the arena in the hopes of stopping the rising rebellion. Even if this twist was planned in advance, it wouldn't have been possible if Katniss had not won the previous year's Hunger Games, as there would be no living female victor from District 12. The 75th Hunger Games were the last Games hosted.

TLDR:

We don't know conclusively, but it's almost certain that the 75th Games (which were planned) were altered to include former winners so as to kill off Katniss (and subdue the rebellion).

Answer:

I think you've answered your own question.

In Catching Fire, following Katniss and Peeta's victories, frustration among the people is growing. They have seen two people defy the Capitol and Katniss in particular is becoming a symbol of rebellion.

Snow wanted Katniss and Peeta killed at the end of the Hunger Games, for their "stunt" with the berries. But Seneca Crane instead announced them as winners (and paid for it with his life). So now Snow is aware that both Peeta and particularly Katniss are symbols, and a threat. The film echoes the book in this regard, and to quote from the book:

...You have no access to information about the mood in other districts. In several of them, however, people viewed your little trick with the berries as an act of defiance, not an act of love. And if a girl from District Twelve of all places can defy the Capitol and walk away unharmed, what is to stop them from doing the same?” he says. “What is to prevent, say, an uprising?”

...

“Why don't you just kill me now?” I blurt out.
“Publicly?” he asks. “That would only add fuel to the flames.”
“Arrange an accident, then,” I say.
“Who would buy it?” he asks. “Not you, if you were watching.”

...

“Only you'll have to do even better if the uprisings are to be averted,” he says. “This tour will be your only chance to turn things around.”

“I know. I will. I'll convince everyone in the districts that I wasn't defying the Capitol, that I was crazy with love,” I say.

President Snow rises and dabs his puffy lips with a napkin. “Aim higher in case you fall short.”

“What do you mean? How can I aim higher?” I ask.

“Convince me” he says.

So at this Stage, Snow wants Katniss on board. He is hesitant to kill her, as it will stir rebellion - but he can't let her "go free", as she will stir rebellion. So he wants her to behave well and do as he says.

Of course, this fails. She pays tribute to Rue in District 11 and sparks visible dissent. A man in the crowd is shot dead and tension is clearly rising.

At this point, Snow is even more concerned. Something the book mentions, which the movie does not, is the following scene which takes place in the mayor's house (during her tour of the districts):

I'm leaving the room when a beeping noise catches my attention. I turn back to see the screen of the television go black. Then the words “UPDATE ON DISTRICT 8” start flashing. Instinctively I know this is not for my eyes but something intended only for the mayor. I should go. Quickly. Instead I find myself stepping closer to the television.

An announcer I've never seen before appears. It's a woman with graying hair and a hoarse, authoritative voice. She warns that conditions are worsening and a Level 3 alert has been called. Additional forces are being sent into District 8, and all textile production has ceased.

They cut away from the woman to the main square in District 8. I recognize it because I was there only last week. There are still banners with my face waving from the rooftops. Below them, there's a mob scene. The square's packed with screaming people, their faces hidden with rags and homemade masks, throwing bricks. Buildings burn. Peacekeepers shoot into the crowd, killing at random.

I've never seen anything like it, but I can only be witnessing one thing. This is what President Snow calls an uprising.

So there is full rebellions occurring now, across all of the suppressed districts. Snow's plan of keeping Katniss "on-side" has failed. Inadvertently, through her tributes to Rue and simply by her being strife is brewing and more signs of dissent are breaking out.

This is when Snow hatches the master plan to send Katniss back into The Hunger Games.

Katniss realises that she'll likely die from this:

“If you're perfectly honest about it, you think President Snow has probably given them direct orders to make sure we die in the arena anyway,” I say.

“It's crossed my mind,” says Peeta.

It's crossed my mind, too. Repeatedly. But while I know I'll never leave that arena alive, I'm still holding on to the hope that Peeta will. After all, he didn't pull out those berries, I did. No one has ever doubted that Peeta's defiance was motivated by love. So maybe President Snow will prefer keeping him alive, crushed and heartbroken, as a living warning to others.

Now, at the start of the Catching Fire novel, Effey tells Katniss "In your very first year of being a victor, you get to be a mentor in a Quarter Quell!”

Our only knowledge of a Quarter Quell comes frmo a recollection Katniss had:

But in school I remember hearing that for the second Quarter Quell, the Capitol demanded that twice the number of tributes be provided for the arena. The teachers didn't go into much more detail, which is surprising, because that was the year District 12's very own Haymitch Abernathy won the crown.

So we know the Quarter Quell is designed to be special. But given Effey's comments, and the knowledge that former winners are supposed to be exempt it seems almost overwhelmingly likely the rules were changed so as to trap Katniss in a situation where she could be killed without sparking further unrest.

Conclusion:

We don't definitively know. There were going to be Hunger Games that year. But it's overwhelmingly likely that the Games were altered to include Katniss.

Some good answers before this one but all of them sidelined one crucial detail or rather person: Plutarch Heavensbee (RIP Mr Hoffman)

After Crane was killed due to the debacle of 74th Hunger Games, we see Plutarch being appointed as head Gamekeeper and a very close associate of President Snow. Plutarch was giving an angry and anxious Snow valuable feedback and advice on how to tackle Katnis and defuse the uprising.

It is only later we find out that Plutarch has ulterior motives in being so close to Snow and the Games itself.

Plutarch has an elaborate plan to take Katnis away from Capitol's clutches.

We also find out that most of the tributes of 75th Hunger Games, all of them being previous Victors, are in on his elaborate plan. It is highly likely that the plan was brewing much before Katnis came on the scene, much before 74th Hunger Games. Because forming an alliance will take much time and effort and trust. They all were waiting for a right time and a right person to galvanize their fight against the Capitol. And since Katnis served that purpose perfectly, Plutarch must have decided its time to implement his plan.

Plutarch knew Katnis enough to know that she was impulsive and brave even under mortal fear. He knew the Victory tour would not go according to Snow's plans, which were suggested to Snow by Plutarch himself. To paraphrase "Distract people with the wedding. Show her as one of us now. They will hate her so much, they might just kill her for you"

So, it is more likely that after Snow's plan, mentioned above, failed. Plutarch convinced Snow that the right way to kill Katnis would be under the guise of another Hunger Games rather than shooting her on point-blank. And since 75th Hunger Games were Quarter Quill, they had a disguise for their plan.

So, it is most likely Plutarch's idea to have Victors as tributes to the 75th Hunger Games and since most are in on his plan, and were ready to sacrifice their life for Katnis's safety, he knew that his plan would work. So he manipulated Snow's decision

In a deleted scene of Hunger Games: Catching Fire (The movie), Plutarch switches the envelope of the original plan for the 75th Hunger Games with a new plan President Snow proposed to him earlier in another deleted scene. After switching the envelopes, he burns the original and puts the new envelope into a vault to be opened on the announcement date. The deleted scene is numbered Scene 84 and is titled Switching Envelopes on the special features of the Blu-Ray and DVD release. Whether this is canon or not, since it is in the film, is debatable, however.

I just wanted to add something regarding the 3rd Quarter Quell and Plutarch. I thought the movie actually did a better job explaining why Katniss was in the 75 Hunger Games than the book did.

In the movie, we get to see things that are happening outside of Katniss' perspective, and it is one of those rare times, IMHO, that a movie improves upon a book.

In the movie Plutarch is shown speaking with Snow and ultimately, we realize that Plutarch is actually manipulating him and pushing him to do things that will actually fuel the rebellion.

IIRC, Plutarch tells Snow that he agrees Katniss should die, but "in the right way; at the right time". When Snow sees Katniss standing up to a Peacekeeper during Gale's flogging, he mentions that Katniss and all the Victors must die as Katniss' defiance has made them too powerful. Plutarch then tells Snow that there is a way for Snow to win (against the growing rebellion) with what the Gamemakers' call a "wrinkle". In the book, it makes it seem more like it was random:

FROM THE BOOK:

Plutarch steps back and pulls out a gold watch on a chain from a vest pocket. He flips open the lid, sees the time, and frowns. “I’ll have to be going soon.” He turns the watch so I can see the face. “It starts at midnight.” “That seems late for —” I say, but then something distracts me. Plutarch has run his thumb across the crystal face of the watch and for just a moment an image appears, glowing as if lit by candlelight. It’s another mockingjay. Exactly like the pin on my dress. Only this one disappears. He snaps the watch closed. “That’s very pretty,” I say. “Oh, it’s more than pretty. It’s one of a kind,” he says. “If anyone asks about me, say I’ve gone home to bed. The meetings are supposed to be kept secret. But I thought it’d be safe to tell you.” “Yes. Your secret’s safe with me,” I say.

Collins, Suzanne. Catching Fire (Hunger Games Trilogy, Book 2) (pp. 80-81). Scholastic Inc.. Kindle Edition.

“Neither you nor Peeta were told. We couldn’t risk it,” says Plutarch. “I was even worried you might mention my indiscretion with the watch during the Games.” He pulls out his pocket watch and runs his thumb across the crystal, lighting up the mockingjay. “Of course, when I showed you this, I was merely tipping you off about the arena. As a mentor. I thought it might be a first step toward gaining your trust. I never dreamed you’d be a tribute again. ”

Collins, Suzanne. Catching Fire (Hunger Games Trilogy, Book 2) (p. 384). Scholastic Inc.. Kindle Edition. [Emphasis added.]

It could be that Plutarch was lying to Katniss in the book, but I think that while fleshing the book out for the movie, the screenwriters stumbled on a more elegant solution.

As an aside, I prefer Plutarch's conversation with Katniss as they dance in the movie.

It is said that Plutarch Heavensbee changed the Quell envelope and burned the original one on the order of President Snow to make Katniss Everdeen go back into the games, as President Snow knew that she was the only female victor in her district.

Also, Katniss was the one who pulled out the berries in the first games in the first place so the President would have wanted her dead.