The plugin adds the 'redirect_to' parameter to all login and logout links in front-end. The value is the URL of the current site. Thus you're redirected to that site after login respectively logout. But if a link contains already a 'redirect_to' parameter, the plugin doesn't change it.
The Plugin affects only the links in front-end. These in wp-login.php and in admin back-end aren't touched.
The plugin hooks into
login_url and
logout_url. Your code has to call functions which make use of that filters. For example
wp_loginout.