Backup won't work unless the security settings allow EVERYONE to access the files

I have a Dell XPS stand-alone PC running Windows 8.1 Pro. My Norton 360 Premium Edition has had no trouble backing up my files on demand or scheduled. I had only one user account until recently. I had to create another account that cannot access my private files. I created an account without administrator access, just "User" access. I've tried various combinations but Norton won't backup unless I have User or Authenticated User in permissions but these also allow the other non-administrator account to have access. 

How can I get my backup to work yet allow no one else to my private files?