I'm assuming you are talking about SyncBack freeware? (You have posred in the Help Files... forum, so it's hard to tell; posting in the forum for the version concerned would maybe have helped
You can run the Scheduled Task under any logon you like (as you probably know) but in SyncBack freeware, the profiles are stored in the Registry under th applicable HKEY_CURRENT_USER, so unless you created the profiles while logged in as Domain Admin (etc), the program wouldn't be able to see them when the scheduler triggered it, and the Task would fail
In SyncBackSE ($$$), by contrast, the profiles are files, stored by default in the AppData area of the user's OS-profile branch (depending on OS in use), but there is an option to store them in the SBSE program folder so everyone can see all of them*. This can sometimes have its own problems (standard users maybe cannot access the Program Files branch) but that shouldn't be a problem with a Domain Admin logged on
BTW, this thread
(and the links in it) may be of interest.
* Actually, you can simply physically move previously-created profile files there from the 'private' location, as the prog scans both locations - it's the location used to save profiles during creation
that the option changes. But I wouldn't like to have to move 600+ user's own profiles there by hand...