Hi Chris, I have the same adapter and have had exactly the same issues as you. It works perfectly on emulators on PC/Mac, but behaves the same when I connect it to my RPie 1. I added the second controller mappings to the cfg file, but only a couple of the buttons work like you.
I’ve seen other people who say it works, but haven’t been able to find out how. Will post anything here that helps if I find it.