Blackflame Covenant + Incinerate

I have the Blackflame Covenant notable and using Ignite from Incinerate.
Incinerate says: "Ignites as though dealing fire damage, every 0.0075 seconds".

I noticed that "Increase Fire Damage" and "Gain as extra fire" nodes are increasing damage for ignite even with a Blackflame Covenant.

Is it happening because "as though" is ignoring conversion from Blackflame Covenant and still dealing fire damage?

And I want to clarify: "as though" counts like "as though from hits" or "as though from damage over time"? Because if it is "from over time" it cannot be converted, but why it contributes to ignite then, if only hits can contribute to the ignite. And if it is "from hits" why is this not converting to chaos. Blackflame Covenant says that Fire spells convert 100% fire damage to chaos.

It doesn't feel right that with Blackflame Covenant both fire and chaos damage are boosting ignite from Incinerate and Flame Wall