Hi Daniele,
You are correct, only
inactive chains are moved to Capacity Tier as described in the User Guide link.
Some periodic full backup, either Active or Synthetic is recommended here for move operations, and consider that you can also use Object Storage repositories as Performance tier as well, removing the need for Capacity Tier in many cases. Since I can see capacity tier looks to be targeting an S3 bucket from a Synology box, I'm guessing you have performance tier as some volume from the same Synology, am I correct? If so, I would advise consider if there's really a need for the copy/move operation if it's going to the same storage ultimately, as it's just excess processing to move the data around on the same server.
If your backup plans require this tiering, that's fine, consider checking if you can configure an XFS or ReFS volume from the share to get
Fast Clone capabilities. With Fast Clone and Synthetic Fulls, you'll get "spaceless" full backups and reduce your on-disk foot print while benefiting from the Move operations as expected.