I was talking with someone and they claimed Item Rarity Support does not work with ignite. I looked at the wiki pages for rarity and Item Rarity Support and was not able to find anything to substantiate this and the person that told me this could not prove a source as they heard it second hand.
Ok so this is complicated.
I'm absolutely not sure how this interaction works with general DoT kills, but in particular socketing the IIR gem into Arakaali's Fang will transfer the IIR bonus to the debuff that the Spiders apply and the IIR will apply if this debuff is what kills. This was a comment made by /u/Mark_GGG a few days ago. Intuitively, one would assume that the IIR bonus would only apply if the Spiders kill, but most of the time Spiders don't directly kill but instead kill with poison, and DoT kills are player kills in terms of attribution.
Now, I cannot tell you if including IIR into the link of a hit-skill that then applies a DoT will apply the IIR to the DoT if the DoT kills for a player situation, but this is a pretty recent comment confirming that, at least for one specific DoT interaction,it does seem to work.
This isn't a confirmation at all for you, but rather just pointing out something a little more recent.
I cannot tell you if including IIR into the link of a hit-skill that then applies a DoT will apply the IIR to the DoT if the DoT kills
I can and it will. All DoT applied by skills have this behaviour, and have for a very long time.