Hola Mert,
I use a plain FTP Account, All is ok said Godaddy. Go Daddy washed his hands of this problem.
I only has a chance, copy all the file generated by Backup Manager (zips and sql ) from the source server and move into /wp-content/plugins/wordpress-move/backup on the target server, then use Migration Assistant/Restore.
Is it correct or are there another precaution? since the are different domains how can I change to the new domain or this is automatic.