This documentation describes the needed rules and rights to allow a user to backup files on the system.
First, you must make sure the user running the backup has the CA Access Control Operator attribute. Next, you will need to create a special program rule for the backup program. Please see below for an example rule.
editres SPECIALPGM ("<backup program path>") owner('nobody') pgmtype(BACKUP,PBF) unixuid(backuser)
Once both of these items are set, you will be able to run the backups without issues from CA Access Control.