There are two types of rewards: individual, and faction. The individual rewards are the jump drives (require kills and rp), custom core ai ships (require rp about their POV in the event), and a custom forum title (requires rp). The faction reward is the shared ships.
Individual rewards are per player: so the player says all the characters they played, and claims all the individual rewards they're eligible for.
Faction rewards are for the whole faction: the 1IC looks at the combined points the faction acquired (at the end of the first post), and lets me know what ships they want.