It's not the best experience. When you install an app, you don't really know where to go to use it. Atleast in Chrome, you see it pop into the apps screen.
If you install the app from its detail page, there is a message telling you where the app now lives. The "Free" install button becomes a "Launch" button that opens the actual executable.
On the search results pages, we don't add any messaging. I've filed an enhancement bug to consider exposing this to users: https://bugzilla.mozilla.org/show_bug.cgi?id=913728
edit: filed a bug