remember-me is implemented through a session instance. And enabling a session instance will always create the cookie, regardless of it's content.
The reason why you are still logged in when you re-open your browser is probably because your session hasn't expired. This is not related to the remember-me function.
The default is expiry after 2 hours of inactivity. If you want auto-expiry of your session when you close the browser, you need to change your session configuration file, and set 'expire_on_close' to 'true' (default is false).