KS fate? Is that even a thing?

The first person who hits an target is marked theirs. If you hit that target first, then you would get the subsequent exp even if the enemy dies.
Even if someone contributes to killing it, the fate itself is considered a groupwide effort to completion.


As the event has now have been active for a couple of weeks, most people have already done the event so fates are more or less empty. If there are a lot of people still actively fighting for the same fate, you can make a party so you all get the contribution shared.