A lot of people complained that the NES Mini adapter doesn't work with Wiimotes. That is absolutely correct and I'll tell you why: NES controllers are designed to run on a 5V bus. Wiimotes, classic controllers, and the NES Mini use 3V logic. I directly measured between GND and VCC on the NES plug when connected to a Wiimote and it was 3.17v on fresh batteries.
I can only imagine the NES Mini must put out a little bit more juice if this device works as intended with original or third party controllers. The Advantage and other vintage controllers with turbo have extra circuits inside them beyond the CD4021 (NES controler chip), so very likely the reason why standard controllers work but not the Advantage or NES Max is the NES Mini *barely* putting out enough juice for the CD4021 to function.
Old controllers need a full 5v source and Hyperkin has cheaped out by omitting a boost regulator and logic level conversion circuitry. So the fact is the old controllers are just barely operating under spec. Good news is you are unlikely to damage anything by undervolting, bad news it is a crapshoot if the controller works at all.
Bad Hyperkin. I would love to know why your engineers thought it would be a good idea to cut corners ike this.