I just started using web app integration for facebook and gmail. The apps work only when gmail/facebook is open in Firefox. What's the point if it only works when the website is already open?
That's how it's intended to work.
If you don't like Facebook and Gmail taking up space in Firefox's tab bar, I recommend right-clicking on the tab and choosing "Pin as App Tab". This will make the tab turn into a small icon, which can't be closed while Firefox is open. It's very useful for tabs you want to have open all the time.