What do you mean by logout? Do you use the session_destroy() function? The session module uses a cookie which contains the session ID. The settings for this cookie can be found in the following php.ini directives:
session.cookie_lifetime
session.cookie_path
session.cookie_domain
session.cookie_secure
They can be read and changed using the session_set_cookie_params() and session_get_cookie_params().
Destroying the session does not remove the cookie, however, if the session is destrotyed server side then the cookie will only cause a new session with the old ID to be created on the next request.
The default value for the session.cookie_lifetime directive is 0 which means that Fx should delete the cookie when the browser is closed - if it is not 0 then you either need to change it or use the setcookie() function to remove it manually when you destroy the session.