The problem with your rule is that the trigger is causing the first action to be true. If the trigger is Jack arrives, when the IF is evaluated, Jack will be present. There is no way to get to the ELSE in your rule.
This is where I use [RELEASE] Combined Presence to help. I've got a virtual presence that is "Somebody is Home" that serves as a master type presence device to trigger based on first arrival or last departure. It works really well for my needs.
