Vortex Traps and Patient Reaper

If I use a Trap support gem to cast Vortex when an enemy triggers a thrown trap, and then the damage over time effect from Vortex kills an enemy, will this trigger the increased life, mana, and energy shield recovery bonus from the Trickster's Patient Reaper Ascendancy Keystone? I'm worried the game won't consider the damage over time effect to be mine, considering it was the result of a triggered trap.

I want to know before I invest time into making a character based on this interaction. Can anyone confirm or deny this?