Advanced instructions for WordPress Multisite installations
By default, all logins need to be submitted via the root site’s wp-login.php page (since that is the only Redirect URL you were asked to submit to Google Developers Console when you first set up the plugin). That should be fine to get you started, so please just try it out, but you may find that users are sometimes redirected to unexpected pages, depending on where on your network of sites they decided to login.
If have a small number of sub-sites, and new sub-sites are not expected to be added often, you might prefer to register additional Redirect URLs with Google for each of your sub-sites, in addition to the root site you were asked to enter when you first configured the plugin.
If you are using ‘domain mapping’ so that your sub-sites are on completely separate domains, you will need to add each site’s login page as its own Redirect URL.
For example, you may end up listing all of https://mywpsite.com/wp-login.php, https://mywpsite.com/subsite1/wp-login.php, and https://mywpsite.com/subsite2/wp-login.php as Redirect URLs in the Google Developers Console.
You will then need to check the box in the Multisite Options section of the plugin’s admin panel labelled Use sub-site specific callback from Google. This will cause all logins submitted to the sub-site they were invoked on.
If you are using the Enterprise version of Google Apps Login, there are further multisite considerations described here.