On my work computer I do not allow automated updates of Firefox.. Instead I use the "notify me" setting and upon being notified I go read the changelogs and manually update. There is no off setting, I wish there was right now as this is not a casual use computer.
What's happening: When you launch firefox it immediately contacts Mozilla to check if there is a newer version. If there is and you use the "notify me" setting you get a popup. You can tell it to ask later and, if you do, it will pop up again the next time you launch the browser.
but... it's doing more than that.
For example. I have several tasks running, one of which plays a small sound file and works as an alarm. The sound file is played via the default windows media player. It works great except Firefox notices this and triggers the popup again. Firefox shouldn't even know that WMP was launched since it doesn't open the browser but it does notice, perhaps because WMP calls home too.
Whatever it is... if there is a way to make Firefox completely stop making connections to anywhere on it's own, including to update the clock, I'd love to know. Surely there is an "I am an adult" way to use the browser. Sadly the about:config settings which accomplished this in the past no longer work.