Is it true that none of the cast knew what to expect in the famous "chestburster scene" in Alien?

It does appear to be somewhat true.

UK newspaper The Independent looked at this legend shortly after Hurt's death and cites an old issue of Empire magazine.

It all started with Scott's desire for genuine reactions of terror. "[They] were going to be the most difficult thing. If an actor is just acting terrified, you can't get the genuine look of raw, animal fear," he mused.

Cartwright, who famously passed out when cameras stopped rolling, said: "We read the script. They showed us a mock-up, but they didn't show how it was going to work. They just said, 'Its head will move and it's going to have teeth'.

Ron Shusett (executive producer/ screenwriter): Ridley didn't tell the cast. He said, "They're just going to see it."

The cast was kept away from Hurt and from the set until the last minute:

Cartwright: They take John down in the morning to prep him and we're upstairs for four hours. We're sitting upstairs and nobody knows what the hell is going on. Harry Dean [Stanton] is sitting in the hall playing his guitar.

Weaver: All it said in the script was, "This thing emerges."

Offal and discarded fish were used:

Scott: Prosthetics in those days weren't that good. I figured the best thing to do was to get stuff from a butcher's shop and a fishmonger. On the morning we had them examining the Facehugger; that was clams, oysters, seafood. You had to be ready to shoot because it started to smell pretty quickly. You can't make better stuff than that - it's organic.

Dan O'Bannon (executive producer/screenwriter): Once the creature was rigged up, they stuffed the chest cavity full of organs from the butcher's. Then they ran a couple of big hoses to pump the stage blood. During all this Ridley moved about, tending to the finest detail. I remember easily half an hour was spent with him draping this little piece of beef organ so it would hang out of the creature's mouth.

This added to the cast's experience:

Cartwright: When they finally take us down, the whole set is in a big plastic bag and everybody is wearing raingear and there are huge buckets around. The formaldehyde smell automatically made you queasy. And John is lying there.

Weaver: Everyone was wearing raincoats - we should have been a little suspicious. And, oh God, the smell. It was just awful.

Then they started filming the scene:

Cartwright: They have four cameras going. You see this thing start to come out, so we all get sucked in, we lean forward to check it out. They shout, "Cut!" They cut John's T-shirt a little more because it wasn't going to burst through. Then they said, "Let's start again." We all start leaning forward again and all of a sudden it comes out. I tell you, none of us expected it. It came out and twisted round.

And Ridley Scott got the reactions he wanted:

Weaver: All I could think of was John, frankly. I wasn't even thinking that we were making a movie.

Ivor Powell (associate producer): I hadn't expected it to be quite that intense.

Weaver: Look, I worked with Roman Polanski on Death and the Maiden - he would shoot a gun off. You can act, sure, but when you're surprised, that's gold.

Shusett: Veronica Cartwright -- when the blood hit her, she passed out. I heard from Yaphet Kotto's wife that after that scene he went to his room and wouldn't talk to anybody.

Kotto: Oh man! It was real, man. We didn't see that coming. We were freaked. The actors were all frightened. And Veronica nutted out.

A well-researched 2020 article offers some more details about how the scene was filmed:

Four cameras were ready to roll for optimum footage. Sigourney Weaver (Ripley) could see the screenwriters huddled in the corner, gleefully awaiting the mayhem to come.

A thin cut was made in the cavity T-shirt so that it would rip easily when the puppeteer below thrust the creature upwards. At first it didn’t come through, so when they tried again the actors were already leaning in, and the amount of blood that burst forth really shocked them. Veronica Cartwright got a face full and actually flipped right over in surprise on the now slippy floor. She realised the cameras were still rolling and had to scramble back in shot.

To have the creature then shoot off across the table, a slit was cut through it, and someone yanked the puppeteer, who was lying on a small camera dolly. The tail whipping back and forth was achieved by inserting a thin tube through it and pumping it with compressed air. It is telling that there are no outtakes of actors or crew bursting into laughter. The atmosphere was highly charged: nothing like this had ever been seen before.

The 2019 documentary Memory: The Origins of Alien also spends quite some time on the scene. Most of what is said aligns with what is said above, but it does add some interesting details:

Cartwright: So we start to roll, and then all of a sudden, Ridley shouts, cut. Cut.

xxxx: It didn't work on the first take. There wasn't much of a chestburster. It couldn't get through the damn t-shirt.

[...]

xxxx: Second time, it still didn't go through, but it came up like that, and then went down and covered in blood. And the actors were all kind of looking like that and curious. So it was a stroke of genius that it went wrong. They still didn't know what was coming.

[...]

xxxx: And this thing goes up through, splat. They fire all the pumps.

xxxx: It was just exactly what Scott wanted. It was just this absolutely immediate visceral response.

Catwright explains what actually happened to her:

I had leaned into a blood jet. That little blood shot me square in the face. And that's when I jumped back and I went, oh my god. And my knees hit the back of those banquette where we were all sitting, and it flipped me upside down. And I said, oh my gosh, we're still shooting. So I rolled over and I got back up, and I ran around and got back into the scene.

(I am still working to correctly attribute some of those quotes, since the persons speaking are only introduced once in the movie.)