how to logout user on browser tab or window closes

I worked long on this one. It is because of the WordPress remember me. Use this code in your theme’s functions.php and it should fix your issue:

function myplugin_cookie_expiration( $expiration, $user_id, $remember ) {
    return $remember ? $expiration : 180;
}
add_filter( 'auth_cookie_expiration', 'myplugin_cookie_expiration', 99, 3 );