Just did an exterminate.
Killed everything waited 7 minutes with th e team.
Not only the acolyte didn't spawn, but the ennemies didn't bother show up either.
So if you put some kind of hidden mechanic like killing x enemy before a chance to spawn, rethink this strategy because if no enemy spawn I can't really do anything about it (and I waste my time).
That's not the first I see that either, got the same thing with a capture mission yesterday, I do my mission and kill everything.
Once I capture, no more spawn, and no acolyte even at the 8 minutes mark.