If you watch from 18-19 seconds into the above video, you'll notice that actually Iceman first pulls up high and to the right -- look at the quick one second of video seen through Maverick's cockpit glass, Iceman's fighter rises up and tilts right.
Then, from 19-20 seconds into the video, there is a wide shot of all three fighters:
Okay, so look at the numbers there under each fighter. #1 is Maverick. #3 is Jester in the smaller plane they are chasing. The one in the middle, #2, is larger and veering off because that's Iceman -- and he's veering up and to the right while Maverick and Jester both continue the slow leftward circular turn they were making through the whole scene.
That's why, as Maverick continues the leftward turn to follow Jester, he sweeps through Iceman's jet wash as Iceman moves up and to the right. The cause of the accident was Maverick following too closely behind Iceman and refusing to back off. He pushed Iceman to move aside but Maverick wouldn't take a less dangerous position because he wanted to hold his spot where he thought he'd get a better shot on Jester.
The accident was Maverick's fault, if anyone can be said to be at fault. I would in fact say that while it was an accident and supposedly just a series of bad luck that had tragic consequences, Maverick was solely responsible for setting those events in motion with his recklessness and his constant behavior of putting personal glory and aggressiveness ahead of more reasonable and careful behavior. It wasn't wartime, and it wasn't a dangerous mission where you have to take risks, it was just his ego and competitiveness that brought about the tragedy.
It's a common theme, actually, to have the hero's hubris cause a major setback that causes him to question himself, and frequently it is some other person who dies or is injured as a result of the hero's failure. Overcoming this loss and learning from it, to become a better and more heroic person, is the point of such tragedy in these stories.