The best way is to just remember to either hit the 'override' hotkey when you switch out, or manually press the stop sign.
It sounds like your F15 key isn't working to stop broadcasting for you. Go into preferences (click the CloneKeys menu in the top left of your screen, and choose Preferences), then click the 'Edit Override Hotkey' button, then press the key you want to set to toggle broadcasting off/on. I recommend a button that you wouldn't normally press. By default it should be the Pause/Break key or the F15 key.
I'll probably add a preference setting that will make it only broadcast when one of the managed applications are foreground in the next version.