Fallen Carnage + Resin / Troll Arsonist + Fallen Hook

Before I invest some resources here, what occurs when you combine these abilities?
If the Arsonist ability kills a creature, does it skip it’s turn and then gain a new turn via the Carnage ability?

Also, the heal from Fallen Carnage when it kills a unit (50% heal) doesn’t proc the Life Mage perk that yields Barrier on heal. Other abilities such as Leech, Regeneration (dodge and gain life), Mend, etc do. Is that a bug or intended?