after logout, get_current_user_id still holds value

Question

I added a login, logout menu item to a menu with the following code in functions.php. After logout it redirects to the current page. But surprisingly enough, the get_current_user_id method still holds the value of the previously logged in user.

add_filter( 'wp_nav_menu_items', 'asv_add_usermenu_student', 10, 2 );

     function asv_add_usermenu_student( $items, $args ) {

              if (is_user_logged_in() && $args->theme_location == 'top_student_menu') {

                $items .= "<li ><a href='" .wp_logout_url( get_permalink() ). "'>Log Out</a></li>";

            } elseif (!is_user_logged_in() && $args->theme_location == 'top_student_menu') {

               $items .= '<li > <a href="' . wp_login_url() . '?redirect_to='.$_SERVER["REQUEST_URI"].'"/>LOG IN</a></li>';
              }
              return $items;
            }

How to grt rid of it ?