Fire exposure support works with infernal hound's aura, it probably shouldn't

Infernal hound aura does not hit, thus fire exposure probably should not work with it.

Fire Exposure support DOES work with it.
Fiery Death support DOES NOT work with it.

Fire Exposure: "Supports any skill that hits enemies, causing it to inflict fire exposure when it ignites an enemy."
Fiery Death: "Supports any skill that hits enemies, causing enemies it ignites have a chance to explode on death."

Above supports have logically identical wording on what they work on. So logically either both or neither should work, and reading the tooltips would indicate neither should. I am aware that 'infernal hound' itself can hit enemies, so they should be socketable to enhance it's melee attacks, but them working on the aura would be weird, and probably wrong.