It doesn't increase death damage; it does nothing. My Skeletal Dragon DoT did 799 damage before the Aura spawned, and 799 damage after the Aura spawned.
If you casted he aura after you attacked, it won't make a difference with spells that were already used before the aura. Aura's only affects spells that are casted while it is up. For example: if I casted poison before my aura, the dot damage won't increase, but if i waited to cast poison, it will do more damage (depending on the aura).
