I have the same problem with a regular bought iPhone that AC+ is not linked to the device yet.
First time for me buying AC+ directly with a product, so I don't know if it should be active instantly.
Normally I got an email with coverage confirmation. I already got an invoice with matching serial number, so I will wait a few days and then call the support.
I just double checked the settings app and while it still showed the offer in the main screen, going to General->About showed it updated with AppleCare+. The main screen still shows an empty spot where the offer used to be now and “null” if I tap it.
Got the email at 11:30 AM, but it’s now 7 PM and still not updated on the About page. Will give it some more time. The coverage now verifies on their website tool at least, so it seems to be officially added at this point despite it not showing on that about page.