My Xbox 360 wired version pad does not vibrate.
If your Xbox One Wireless Controller is not vibrating even with the vibration setting turned on, the controller might need to be charged.
So did you notice what's wrong here ?
And what's with the Reliable Permit Solutions, LLC you linked ?
We don't need any trucking Permits here !
Maybe there is a Problem with the latest Version (8.1.1) of Recalbox
It says that the last Version of Recalbox the Xbox 360 Controller was tested with is 8.0.0
Maybe you should try to rest your RecalBox to Factory Settings and see if the Controller works than.