The only times it should matter are when somebody would get a distinct and quite possibly relied-upon benefit for the kill. Notably
- if you keep killing biotic charge targets, the vanguard may end up in a bad position with weaker shields than expected
- vorcha and krogan need to keep killing for rage
- if there's a group and you killed the one target which was primed, you may have saved the others from an explosion/burst, so you probably should instead have targeted somebody who wasn't primed.
Anything else... well, you may slow down somebody's challenge progress but you're not actually hurting their performance.