Crafted Eternal Chilling Darkness today.
It does not trigger off of damage from either death aura or negative energy burst. This includes both the damage to myself which heals me as well as damage to surrounding enemies, which I would think should count.
It does trigger off of necrotic ray and the damage from finger of death whether mobs save against the death effect or not.
It still seems quite strong because it triggers off of finger of death, but it would be improved if it is fixed to work with death aura and negative energy burst.
I've filed a bug report and posted a thread in the general forum here.