Volatility + Embitter: does it work?

I'd appreciate some help here.
Leveled a Pland Chayula Monk. Volatility gives % gained chaos damage.
So I thought about using the Embitter support to convert that gained chaos damage into cold.

The tooltip doesnt seem to include volatility at all. And while I can freeze rares (from other sources of gained damage as cold) I was never able to even slightly trigger the freeze buildup on bosses.

My conclusion is, you cant convert the volatility chaos damage to cold with embitter. But I would love to have it confirmed by someone and hopefully explained, why its not working - at the end, I want to learn about mechanics :D

thank you in advance