I believe you would have to configure it on a per-game basis.
Very easily, through the config menu you'll be using often with this device. And you can base new configs off of exported configs, so you can always go find an earlier, simpler bind with the swapped buttons that you had saved to make the process faster.
However, I think it's common for most SC users to map A and X to left and right grip, respectively. It works really well, since players tend to use those buttons so frequently. I tend to keep it like that, and use Y and B for secondary actions. Play around with it, though! Find what feels most comfortable.
Thanks. I'll give it a go once the controller arrives.