I've never used a gamepad for Jedi Outcast, let alone a modded Xbox one, but I would suggest a few things.
1.) Check Yoda's Help Desk at the support section at Lucasarts.com. Even if you have a custom gamepad, it may be a universal problem.
2.) Re-calibrate your gamepad from the Gaming Options section at the Control Panel. I've had a joystick which straight out of the box it kept rotating left and down.
3.) Google your problem
That's all I can think of, sorry.
Edit: Come to think of it, you could also buy a regular double joystick gamepad. I've seen them at Walmart for 15 bucks.
Also, the new Xbox360 controllers are compatible with the PC straight out of the box through the USB attachment. They are around 50 bucks. (I've never seen one before, but thats what I hear.)