If I have an active Spiritomb AR with 5 damage counters on it and I use the attack Darkness Grace to evolve a Nidorina into a Nidoqueen RR, is my Spiritomb knocked out? I would assume so. but that'd be cool if it didn't.
You finish all effects of an attack before the turn ends.
So the damage counter is placed before the turn ends. Spiritomb is KO'd at that point.
It's already discarded by the time the between turn phase occurs.
