When a user with a roaming profile logons on to a computer and is authenticated to the domain, a copy of the roaming profile is pulled down from the server to the local machine. This is why you will see a profile with the users name stored locally. Having a locally stored copy of the users roaming profile allows a user to maintain all common settings (minus any changes) should the server hosting the roaming profiles become unavailable.In this event the computer simply loads the local copy. Without a stored local copy the user would then be logged on using the default user profile for that computer and loose all of thier custom settings.
The advantage of roaming profiles is to allow a user to logon to any machine on a network and always have the exact same profile configuration where ever they go.
As for deleting a profile upon exit, personally I know of no way to do that. I’d suggest doing some research on the subject as maybe there is a way to accomplish your goal.