Hello!
What relic did you use for it?

Also on what hominculi did you test it?

I played samurai and used magic hairpin.

Magicite Hairpin: "Each time an enemy is defeated, the time until a cooldown ability can be reactivated is reduced by 30%(40%)"

That means you can get your reactivate faster every time you kill the enemy. It doesn't work like a passive skill.

If you want to get passive cooldown reduce, you need to use "Eye of the Ancients", it gives 15-25% of reduce constantly.