Sorry, need to revert, the affected network uses Meraki Managed Owners.
Thank you for trying to help me, but that's not the point.
Users are already set up. They have to authenticate themself upon enrollment, regardless they are coming over DEP or BYOD. The only difference between these two methods.
When coming over DEP, Meraki checks the device, checks authentication and assigns automatically user to this device, so user tagged profiles are getting installed.
When coming over BYOD, Meraki checks the device, checks authentication but doesn't assign user to device, so user tagged profiles aren't getting installed until we manually assign user to device.