Trickster - Patient Reaper and Oro's Sacrifice

Was wondering if these worked together or if the culling strike would cancel out the Patient Reaper?

Basically wanting to make a flicker strike regen char using ignites to proc

Patient Reaper -

50% increased Damage over Time
Recover 2% of Maximum Life on Kill
Recover 2% of Maximum Energy Shield on Kill
Recover 4% of Maximum Mana on Kill
70% increased Recovery Rate of Life, Mana and Energy Shield if you've Killed an Enemy affected by your Damage Over Time Recently

want to use Oro's, but it has "Culling Strike against Burning Enemies", but im wondering because of how path's wording is so important if it would still work from the culling strike because its specifically "against buring enemies" so would i still receive the "70% increased Recovery Rate of Life, Mana and Energy Shield"?

If you use culling strike to kill a burning enemy, that counts as killing an enemy affected by your damage over time. As long as you were the one who inflicted the burning, of course!