@Melissa,
This seems to be my experience as well, although my experience is limited. Here is my scenario:
I had an iPhone 6s that was unsupervised and unmanaged. I backed up to iCloud.
My new iPhone 8 was enrolled in DEP and assigned to Meraki with a Supervised/Mandatory profile. In going through initial setup on the new phone, I chose restore from iCloud. After completing setup, the device was not supervised or managed, and I never received any screen that would indicate anything was coming in from DEP. So, I did a few experiments.
1. Updated iOS on the phone, wiped the phone (it kept the iOS update) and tried the restore again. Didn't make any difference.
2. Ran through the setup on the iPhone 8 without a restore. Phone was Supervised and enrolled and Meraki app pushed as it should have been.
3. Wiped the phone and tried with the restore again. Still no go.
4. Restored the same backup to a DEP Supervised/Mandatory iPhone 6S instead of the new iPhone 8. This WORKED!
5. Backed up from this now Supervised iPhone 6s to iCloud.
6. Restored from this supervised backup to the new iPhone 8. This worked.
I'm thinking something new was introduced with iPhone 8 that prevents the DEP push when restoring from an unsupervised device.
If someone else has the equipment to try the same experiment, I would love to see if my scenario can be duplicated.