So a small update for anyone who would ever find himself in the same situation.
I've opened a Tadarr feature request as the 'Move' Radarr does seems to be a copy & delete.
This makes my home server download the file and re-upload it. If I just execute a script it works perfectly.
Only thing being is that the script gets executed after Radarr downloads and uploads the file.
So this seems to be something a bit more suited for Radarr/Sonarr discussion as the rclone I currently use does what it's supposed to do.