The problem here is browser behaviour. Cookies aren't usually destroyed until the browser is closed, and PHP sessions are maintained via a session ID cookie.
Your best bet may be to set the session timeout to something shorter than the default (15 or 30 minutes I believe)
You could try and do something with onunload as Anonymous suggests, but the onunload event is not guaranteed to fire so you won't be certain that the session has been destroyed.
Is there a particular reason you need the session to be destroyed straight away? If we know your exact problem we may be able to suggest a workaround