Anytime infernus ult is on cooldown, it remains on cooldown for the given time, even when cooldown reducing items are bought. This behavior is also seen when he upgrades his ult to tier 2, where the cooldown will stay the same until it is completed, then being reduced for future uses of the ability.
After using the ult it stays on the base cooldown, even after punching the fast cooldown option. using ult with fast cooldown already on seems to work fine