When a Constituent's address is changed in Luminate Online, the sync will update the address in Luminate CRM and add the previous address to the Related Addresses list, which occurs whenever the contact address in Luminate CRM is updated.

The Primary checkbox on related addresses is completely independent of addresses that are added to the Related Address via the Integration Sync. 

Additionally, the new address will not be added to the Related Address list until it is changed.