This code snippet will detect the user's site automatically on login and redirect to respective site after login. For WordPress MultiSite only.

rups_on_login.php

<?php
function go_to_primary_blog($redirect_to, $request, $user){
$user_info = get_userdata($user->ID);
return get_blogaddress_by_id($user_info->primary_blog) . 'wp-admin';
}
add_filter("login_redirect", "go_to_primary_blog", 999, 3);