@StephenB - I can confirm that - *.TMP files are getting created by the NAS
No, they are left behind by the PCs (most likely by office).
If they were created by the NAS, they would be popping up even when no PCs were connected to the NAS. You can confirm by creating a test share that the PCs can't access, and you will find that no *.TMP files show up in them. You can also look at the creation times of the files, and confirm that they are being created during working hours.
From what I've read, the problem occurs when the PC user is editing a file that is owned by someone else, and they don't have the rights needed to change the ownership. In particular, the PC user needs modify permission.
Try going into a share where this is happening from a Windows PC, and right-click a file or folder inside the share (not the share root). Then look at the security tab, and see if "modify" is set for "Everyone". It likely will take several seconds before the security checkmarks are filled in by Windows.
You are confusing the files being created by the NAS for those being created or just left undeleted because of the NAS (but by the PCs). There is a huge difference between a shared folder on a network device and a local folder, though the system tries to make them look the same. One of those main differences is permissions, which Samba must map between the Linux core of the NAS and Windows. Until you realize this difference and start looking in the right places (where @StephenB has pointed you), you'll never find the problem.
In addition to looking in the security tab, look in the Details tab for the owners of the .tmp files. That will help you track down which users permissions are likely causing the issue.
Permissions issues can pop up when you add users to an existing share, especially if they are not a part of the owning group. Resetting permissions in the share can help make existing files accessible. But if it continues to happen on new files, you have more work to do sorting out the permissions problem. If you try and change permissions via Windows (in that same Security tab), that can add yet another layer to decipher.
Of course, similar issues can happen if one user has a file open when another tries to save it, but Windows/Office normally warn about that when you open the file.
