Jarvan IV and His Dying Ult

Same way for most every other ult/ability that has a travel time like that, the ability was casted and then killed afterwards, so because the cd starts after the cast it is left on cd.

The only exceptions to this I can think of are specific mentioning that the ability would act otherwise.

It's a known weakness, as the game progresses I assume you launch your ult early to force early flash and escape cooldowns

But it does lose usefulness the weaker you are too

when talon dies mid ulti, his Blades do not converge.

Many champs have similar weaknesses.