Had the same problem. I bought third party controllers and both were recognised as XBOX 360. So they didn't work via USB.
And here's the story. One of them, when You'll press combination of START+SELECT buttons switches it's mode from XBOX to Nintendo (left and right diode changes to the second from the left). From that moment using it with USB cable was ok, the next problem was BT pairing.
I switched the driver to automatic, entered pairing mode and had some tries with using reset button (the hole at the back of the controller), pressing P3 button at the same time, unplugging and plugging USB cable, finally making the device connected.
The second controller from the same vendor is not working at all, USB or BT. It works with PS3 Console, but no luck with Recalbox (I'm using 9.1). My guess is that the same hardware uses different firmware inside.
Maybe someone find this information useful and save some time and nerves trying to make work something that will not.