Caitlyn Ult icon not resetting on teammates HUD's

I was playing Caitlyn on live servers and cast my ult on the enemy Lee Sin. Lee died before my ult left my gun and went onto a 5 second cooldown. My duo and I continued playing in lane and he mentioned not being able to finish a kill because my ult was on cooldown but I already had my ult back up after waiting the 5 seconds. On my screen, my ult was ready to be cast but not on my teammate's screen.

Step one: cast caitlyn ult Step two: kill caitlyn's target before ult finishes casting Step three: wait a couple seconds until caitlyn's ult comes off of the short cooldown Step four: check caitlyn ult icon on both caitlyn's screen and her teammates' screens. Caitlyn can cast her ult again but her teammates see her ult is still on cooldown next to her icon