Currently browser.js handles hiding any current notifications when the user navigates away from a page. It also only does it for the currently displayed browser. It makes more sense for tabbrowser to handle hiding them since it is the one that creates the notificationbox in the first place. I think it should also do it for background tabs too.
Bug 839516 / bug 846754 fixed the "background tabs" aspect. I don't think tabbrowser creating the notificationbox means that it needs to be responsible for also hiding it across page loads, so I guess I'm suggesting WONTFIX.