Further resolution.
I have done several things and now have fully functioning backups that are user-specific with adequate security.
1. Eliminated the user name "Admin" and "Administrator" from all machines. Administrator accounts now have different names and different full names. Each machine now has a unique administrator name.
2. Eliminated the volume_1 share from the NAS and established a share for each computer.
3. Created a user on the NAS for each Win 7 admin account. You must name it with the exact name of the account and use the exact same password.
4. Since this is Win 7 Professional, backup can be done from the Win 7 backup utility directly. This is actually quite functional and backs up all users from the admin account. Works quite well.
Easeus Todo backup will not work with Win 7 and this NAS, at least in the current form.
I hope this helps others struggling with this.