Hello @pautgn,
If the source and destination domains are different, SiteGround Migrator will update all URLs in the database to match the new domain. The plugin will not only change the home and siteurl values, but perform search-replace too.
After you initiate the transfer, SiteGround Migrator will perform its checks and will notify you that the destination domain is different. Here you can decide whether to cancel the transfer or proceed with the primary domain change.
The full migration process is described in detail in this tutorial.
Best Regards,
Kuzman Stoyanov