How did Lamar Burgess instigate the red ball?

While I'm skeptical about finding a completely plausible explanation, I don't think this is completely wrongly done.

The fact that the prediction itself has put the events of the movie into motion, does not mean that none of this would have happened without it. There were many ways in which Burgess could've set Anderton on his path. Once that's set up, the future murder is going to happen, and the Precogs see it. Then Anderton follows the prediction, which kinda helps him arrive to the right place.

The fact that he also arrives at the same time can be attributed to the movie magic, but don't remember that he saw the time and was chasing it.

We can also view it like this:

1. The future murder is set, hence it will happen.
2. Therefore, Anderton will find out about it and will pursue the trail.
3. Because of that, the events will happen as we saw them.

So, the Precog's vision, in a way, contains itself, but did not initiate the events. It possibly shaped them to an extent, although I wouldn't bet on it.

Napoleon Wilson nicely put it in the comment, so I'll copy it here, as it is really a summary of what I was trying to say with the above:

Once Burgess set up Crow, the "murder" by Anderton had to happen sooner or later anyway, it's just that the prophecy made it unneccessary for Burgess to give Anderton any further clues.

The part of the murder that we saw in the precognitive vision happens the way it was foretold. The vision does not show Anderton seconds before it. I think that the way the murder/suicide was shot clearly shows that it fits the vision.

Of course, the time is off by a few seconds, but the pictures that Precogs get are not a tidy movie. The clock could've been from a vision a few seconds before the fatal shot.

There is one more factor, which Agatha explains: once you know your future, you can change it. Anderton decides against killing Leo who, in turn, reveals his true motivation and initiates his murder/suicide.

This brings us to one point that I think the movie maybe silently claims (as discussed in the comments, I'm not too sure of this part, but I see it as a possible theory): you cannot change major moments of your future (similarly to Sliding Doors). This premise, I think, would give an extra ground to the assumption that, no matter what happened prior to it, the murder would go on as the Precogs foresaw, so it was in no way initiated by them.

This thread is a few years old, but I just re-watched Minority Report (I think it's a truly great movie) and I have been thinking about this presumed paradox ever since.

I don't think there is a paradox at all. My reason for this is best explained by pondering this key question:

What is the incident that sets the entire plot in motion, and who instigates it?

The critical juncture occurs 29 minutes into the film, when Agatha, the most gifted of the Pre-Cogs, rushes up out of the water in the Temple, grabs John Anderton's arms, and says, "Can you see?!". She then broadcasts Lamar's murder of Ann Lively (her mother) from years before. It is this cryptic video of Ann Lively that sets everything in motion: John Anderton starts to follow the clues that will lead inevitably to his discovery of the murder; and it is this investigation that causes Lamar Burgess to pay off Crow and frame John Anderton.

Agatha is the key to all of this. She instigates the entire plot, and given her abilities to see the future, intervenes where necessary.

Why does Agatha reach up out of the water and provide Anderton these clues to her mother's death? The motivations are obvious to me: she wants justice for her mother's death, and freedom for herself and the other pre-cogs. Agatha knows the future: I believe that she knew full well that her sudden and unexpected choice to reveal her "minority report" to Anderton would set the dominoes in motion that would lead to her freedom, and justice for her mother.

This still doesn't explain, however, why Anderton ends up in a random hotel room, ready to murder someone he has never met before. Again, Agatha is the key to this question as well. It is Agatha who cleverly helps Anderton evade capture by the police, and then guides him directly to the hotel where Crow is waiting.

I love this subtle aspect of the plot, which reinforces the main theme that "everyone has a choice" and that nothing is truly pre-destined. John Anderton chooses not to murder Leo Crow; Lamar Burgess chooses to commit suicide; and Agatha chooses to set everything in motion, when she reaches out and reveals to Anderton her minority report of her mother's death.