This was out of character for Kakyoin, who'd never acted like this before. It's not crazy to assume that if Kak also acted like an asshole Jotaro'd not react like he did.

To be far in this case most people Jotaro beat he probably beat only half to death, thus hospitalizing them. In this case, Kakyoin (aka Mr. Flubber) was performing a back breaker and was gonna kill the dude at that rate. I think killing could be considered as going too far.