In a game we are playing, a Cylon player activated the Besieged crisis card, which states that after the raiders have been setup, they immediately get activated. However, another player is using Apollo, whose ability states that when vipers are setup, he may immediately hop in one and take an action. Apollo wants to attack, so who goes first, the raiders or Apollo?

My guess is that Apollo would go, then the Raiders. Other than a hunch, I have no actual reasoning to back this up until I can get home and reference my copy of the game.

Vipers are setup as part of "phase 2 - setup".

Raiders are activated as part of "phase 3 - special attack rule".

Apollo would go first, I think.

I agree, Apollo gets to go first. Its a very interesting scenario though.