First, do not use "mixed" security style. Ever. It only leads to problems. Use the permission style of the majority of users/accesses. When in doubt, use NTFS. But not mixed.
Second, you need something called "user name mapping" configured on your cDOT system, where you map UNIX users to Windows users. This is a required step. You can read about it in the NFS File Access Reference Guide (here) and in the CIFS File Access Reference Guide (here). Note that it might be a bit much to take in if you're completely new to ONTAP.... Your partner that sold you the system should be able to help you with the implementation