On the logout page is code to unset the session variables. If the session variables are no longer set then you should be logged out. In the default URSP files the admin login does not contain any cookie references, it just works with the posted values from the admin login page.
Once you go to the logout page you should be logged out. If you are still logged in after you go to this page there must be something setting the session variables again. Please post back with a current copy of your admin login page and the logout page you are working with.
A good way to see what is in the session when you are on the login page is to use a vardump like this to see all of the values:
You can put this in at the top of the page to see the values, this will let you know just what is in the session.