I feel like I've just explained how it works lol. A poison kill is a 2-stage kill. It has to first be applied, and then a cycle later, it processes, resulting in the victim's death. if someone is immune to kills, then the poison will fail from the start, hence why you see failed. If you don't want to accept my explanation, that's your call, you can check with the hosts, but that's the only way I've ever known Poison Kills to work.
Brann's beard is the greatest killer of them all.