There must be some additional context here. I've never observed this behavior on Windows or on Linux (although on Linux I'm using an LTS release, which could be a confounding factor).
Obviously this is only a problem on Linux, because on other platforms Firefox's own autoupdater will only apply the update when Firefox is restarting.
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).
I do applaud firefox for supporting so much customization, as in this case. If I weren't able to disable this behavior I would have stopped using firefox immediately.