Hello,
You can try to login the user through his $user_id. So your code will be:
$user_id = $this->user_model->addUser($user);
$post = array('password' => $pass_for_auth, 'email' => $email);
Auth::loginUsingId($user_id);
You created the user so it returns an user_id, with the user_id you can login the user.
Hope this works!