Yeah, that's bound to happen on Linux if you run an update while Firefox is open. Being able to continue running while all your files get switched out from under you is a pretty big thing to ask from a program and I think they were having issues with crashes and risking corrupted profiles, so they made it do that just in case.

In my experience, running software updates while using the system is a pretty bad idea in general. It works well most of the time, but there's a reason Linux* is the only system that allows that (every other OS defers applying updates to a reboot).