Irregardless of the use cache setting, writes to user shares will tend to spin up disks, as the system has to check to see if the folder and file being written to already exists on the array so it can overwrite if necessary.
Installing dynamix cache dirs will mostly alleviate this.
As to it rewriting vs simply moving, this is because sonarr is moving the file from (as far as its concerned) /downloads to /media. Since those are two different mount points, any OS will do a copy / delete operation instead of a simple rename to the new folder.
How to alleviate this is to instead of passing through /downloads and /media is to pass /mnt mapped to /mnt to all the apps involved and then reference within each app's settings (sonarr and your dl client) /mnt/user/...