thanks for reporting.. that is really strange do you use a xbox controller? When I am conntecting my controller everything is running properly and I do not move without moving the joystick... maybe try to switch the two joysticks in the input settings when you start the application.
Viewing post in Suggestion or Bugreport comments
If the problem remains then I think it has to do something with the called "input dead zone". Quick explanation.. Some Controllers have an idle input of up to 0.3 which causes the player to move without any "known" input.. However that is a bit harder to fix because I am not able to let the users individually customize this dead zone.