I don't recall ever being forced to restart Firefox. It just puts a message in the menu that says "Restart to update Firefox". But I can let that sit there as long as I want.
EDIT: Actually just looked it up and I see how you could have the issue. If you're using your package manager to update instead of using Mozilla's updater, then it will perform the update without accounting for whether or not Firefox is running. That means that the next time Firefox loads something from disk, it will mismatch with what the running version expects.
EDIT: Actually just looked it up and I see how you could have the issue. If you're using your package manager to update instead of using Mozilla's updater, then it will perform the update without accounting for whether or not Firefox is running. That means that the next time Firefox loads something from disk, it will mismatch with what the running version expects.