If you don't find what you need here, check out #beholderveekubuntuguides , there might be the thing you're looking for.
Here's the full guide on setting up the Steam Controller, but if you have this particular issue, this mini-guide is for you.
If only keyboard and mouse controller bindings work in games, but gamepad bindings do not, a possible reason might be that you did not put your own Linux user name in lib/udev/rules.d/99-steam-controller-perm.rules where it tells you to. Check the file, you'll see the place in the first half of it.