Kill attribution with Contagion spread

When a monster is slain by Essence Drain or Blight of Contagion that has spread through Contagion, which skill is considered to have killed the enemy?
Is the kill attributed to Contagion, or to the spreading skill itself (Essence Drain / Blight of Contagion)?

I understand that the actual damage killing the monster comes from Essence Drain or Blight of Contagion.
However, since that damage is being spread by Contagion, I’d like to know for sure which skill should be linked to Item Rarity Support.
Should Item Rarity Support be linked to Contagion, or to Essence Drain / Blight of Contagion?