That's a bit of an edge case, and open to your interpretation. If all Harm is dealt at the same time, than you brought the necromancer to 0 at the same time as they hit you. Since the healing doesn't happen until after the harm is dealt, the necromancer is already at 0, and would be considered dead.
Thank you! I initially assumed that would be the case, but then I started confusing myself.
I'm sure I'll end up doing it again with other enemies, so just for future reference:
If enemy special abilities/traits don't specify timing, does the action take place during the same round/right after Harm is dealt, or does it happen in Step 2 during the next round? (I know it's pretty much the same thing, but I have a weird brain, sorry!!)