I had to test it out myself to see what was going on, and couldn't get it happening. I never play split screen so I never noticed before.

Tried going a little early and a little late as well as on time, but out of the 5 or so attempts I tried, nothing worked, with either player 1 or 2.

I never miss a boost start normally so I'm guessing you either just can't, or the timing required needs to be incredibly precise.
Since the game is running at 30fps, it could be something to do with that instead of the typical 60.