Every time a group is added to a page or a channel, it will be updated and added to the update cycle. This update makes sure that all group members are correct, including nested group members. The group sync cycle runs continuously, but may still take up to 24 hours to complete. Usually this is much faster, but 24 hours is a good thumb rule.
If you need to make sure group members are synchronised immediately, you can open the group in the user search. From here you can open the more -menu and click "Update group". Please note that this function is only available to admins.