Contagion, Essence Drain, Item Rarity Gem

I may need a refresher on the gem and dots but if I remember correctly the first time stamped DOT effect on a monster counted for IIR (Correct me if I am wrong).

So what happens when contagion linked to IIR spreads itself with a non IIR linked essence drain?

Which is awarded the kill? Does the monster get the boosted Item Rarity?

That's actually a good question, we know that DoT which was applied to the target first gets the kill and we assume ED and Contagion are separate DoTs because the game doesn't sum them up.

So, we have four possible scenarios:
* You cast contagion on an enemy and follow it up with ED, that one is clear enough - Contagion gets the kill.
* You cast ED and follow it up by Contagion, also clear - ED gets the kill.
* You inflict a target with Contagion and Essence drain gets proliferated on it from another enemy - also fairly clear, Contagion.
* And we have the last one which is a bit muddled, an unaffected enemy steps into the pack and gets Contagion and ED proliferated on it, it can go both sides here but I'd assume Contagion has priority.

contagion has the spread function so Id also assume that it is the first on "at the same time" list

What would you expect to happen if contagion is applied first, followed by essence drain, and then contagion is re-applied (before the original fell off)? Since contagion has been on the longest, but not "that" contagion. Not sure what I would expect.

I tried to test it and confirm, however DoT can't trigger Innervate on kill so I'll have to think of some other way.