I've found that more often than not, the DEP device isn't recognized and doesn't install the config unless I first Set Up As New Device. So here has been my workflow:
- Make iTunes backup of old phone.
- Power on new phone and update via iTunes.
- Go through setup on new phone and choose Set Up As New Phone. When I do this, it properly retrieves configuration and prompts for User Affinity login info. At this point, I can then just hit the Back button and go to "Restore From iTunes Backup".
- After I restore from the iTunes backup everything works just as it should.
In summary, I've just had to do "Set Up As New Phone" once to get it to recognize it as a DEP device. After that, you can restore the phone or just hit Back in the setup to restore from a backup.