Potential Damage Conversion Bug with Pyromantic Pact

On my Infernalist, I have the Chaos Inoculation passive and the Original Sin Amethyst Ring. My expectation was that this would allow me to eliminate the damage I take from Pyromantic Pact by converting the Fire Damage to Chaos Damage and then being immune to Chaos Damage. However, I found that I still take Fire Damage from Pyromantic Pact despite having the ring.

This seems like it could be a damage conversion bug. If not, then maybe it would help to adjust the explanation text on either the Pyromantic Pact passive or the Original Sin Amethyst Ring to clarify why this damage conversion should not be expected.

Pyromantic Pact isn't damage dealt by you, or else all your damage modifiers would multiply it and it would pretty much be an instant kill every time. Original Sin converts damage you deal. It does not convert the damage you take.