That is the way it is supposed to work.
the remember me and auto login option stores the username and password in a cookie.
The logout page deletes the users session, it doesn't delete the cookies.
when the user visits the login page, the cookies are still set, so the user is logged in and a new session is created.
the user would need to remove the cookies from the browsers cache to stop the auto login from logging them in, it is not dependent on the logout page.