But if you’re using the built-in auto-updater (like people tend to do on Windows and macOS), then it happens automatically in the background, unless you tell the auto-updater to not update automatically.
Definitely does not work that way on my Windows 10 installation. When update is available, Firefox will have a “Restart to install updates” in menu button notification - but the files are not replaced on disk until you actually close (or restart) Firefox and thus Firefox continues to work normally.
What can happen though is that if you run another instance (ie. another profile) of Firefox while the first one has “staged” the update then that another instance can trigger the files to actually be replaced on disk but you would very deliberately do that.
Doesn’t really sound like a company that I would want to do any business with then.