I did as you asked, but sadly even if now that the problem with the menu stopped, my character still circle while aiming...
Are 'Analogue Aim' and 'Analogue Right Joystick X' set to the same values?
If not, there might be an issue with your R-stick. PS4 controllers often will read values from the R-stick oddly I've found. They don't zero out correctly. Try disconnecting the gamepad and reconnecting with the sticks in the center (as best you can). Also make sure you don't have any secondary remapping software running. And then in game once it's started waggle the stick slightly which should zero it out.
If that doesn't work, there's not a whole lot more I can do for ya as I don't know your controller setup.
As stated before we are going to be releasing an update soon that has upgraded controllers support. Although if your problem is related to a remapping tool or anything, there isn't a lot I can do about that even in the newer version as it's related to the controller and not the game.
Either way, expect a beta version of this update in the next week or so. The artist is currently doing a polish pass on the lighting.