This add-on is most useful among other similar ones with such function. It certainly stop working when you are not browsing to the top. Only minus is... it somehow erases already displayed old tweets while working on tweet search tab (or maybe it is just Twitter's fault).

Watch tweets as they are posted, or scroll down a few pixels to stop the automatic feed. It does what it says it will do, seamlessly.

If you're like me and like to keep an eye on your Twitter feed while you work, this Auto-refresh Addon will give you a hands-off scrolling feed that works well and causes no apparent lag.