iPhone private MAC address not working? 2 MAC addresses appear in my router

I just connected my iPhone to a brand new router and saw that 2 new MAC addresses appeared in connected devices. By disabling the "Private address" feature I could verify that both MAC addresses belong to my iPhone. I understand that this is a privacy feature, but what's the point if my hardware address shows up anyway? This was my first time connecting to this network and the private address feature is enabled by default. I have tested this on 2 routers, same thing with this iPhone. However, when using an Android device with the private address feature, only the spoofed MAC appears in my devices list. Wonder if this just happens to me or also to others. And, more important: How can I prevent this from happening?