
The Xbox 360 controller has a player indication light which ideally tell you the controller number. Unfortunately, Unity doesn't listen to this at all.
For example, the joystick shown above says that it's connected to the computer as controller # 2. However, when testing this controller in a Unity game, it's very likely that this controller won't move player 2 (whose green in my demo scene).
From my test, it depends on an unknown order in which you plugged your controllers. I've seen controller # 2 move player 1 (the red character in my scene) when I had two controllers plugged in. Although I was testing this on Windows, I'm sure the same problem will occur on other OSs.
The best work around for this as of now is to simply ignore the player indicator light on the Xbox 360 controller when playing Unity games. Unfortunately, I'm sure this will annoy end-users.