I just tried that controller today at a store and confirmed the issue with the dpad detecting inputs on a different button if you're pressing towards it (like pressing the top of the side buttons does an up press)
but it's weird, I played bananza and in that game you can open the skill menu with up and photo mode with down, pressing the side buttons in the up and down edges didn't trigger either menu, however, in the skill menu, pressing the sides in different up and down edges did constituently trigger up and down inputs
I'm not sure if it's meant to be like that, does anyone know more about this?