Security best-practice is to never use the untagged (native) VLAN. The number of organizations that follow this best-practice is probably under .5%. Since it's something that's rarely practiced, it's no surprise that Cisco has examples with the manager interfaces being untagged.
I have used untagged VLANs on the management interfaces for all of my installations. There is nothing wrong with this deployment - it will work just fine. Your other VLANs will require tagging. I'd recommend keeping your Manager and AP Manager interfaces on the same VLAN, though this isn't required.