There is some server delay, but also the damage isn't subtracted from the boss's health until after a battle finishes. So if the first player to deal lethal damage doesn't use the Skip button and has fast forward off, then it's more likely that additional players can join and deal that same lethal damage.

I'll do this intentionally sometimes if I know I'm going to kill off a boss, but I want to increase the chances of another player joining to get credit.