What it sounds like you did was go to something like and logged in to download and install an MDM profile. That's your Jamf Pro server in this case, but could be any MDM that supports the automated device enrollment process. The device 'phones home' to Apple, and Apple's servers see that based on that devices serial number it should be redirected to enroll in an organization's MDM server, and then does that. DEP, or rather Automated Device Enrollment, as it's now known, kicks in when a new device (Mac or iOS) or a wiped device connects to the internet for the first time during initial setup. It's still considered 'user initiated' even if you as a support tech do it.
What you're describing is not a DEP enrollment, it's a User Initiated Enrollment.
