That's probably your problem. You backup user is writing files which have various Pi user and group id's to the NAS, and the NAS stores those ids, as otherwise every file would belong to the backup user, which isn't what you want.
But the NAS doesn't know about those users and groups, and their relationship to the backup user. To allow the backup user to access those files, they have to be set to world readable and writeable i.e. 777
If you created matching users and groups on the NAS, and made sure the backup user was part of those groups, the NAS would then know who was allowed to access what, and the file permissions could then also be stored correctly.
This is my interpretation of how NFS works, I may be wrong.
---druck