How do you know what the voltage is with the truck running. I would not rely on the VOLT meter in the truck, if this is what you are using to determine if the Alternator is working correctly!
I have a device that provides a voltage read out when the key is turned on and when the Alternator is providing current. This is plugged into the cigarette lighter, providing hands free phone use thru the radio. Since my truck is a 2008, and during that time period the standard radio did not offer pairing your phone to the radio. The device is a Nulaxy KM 29 transmitter which provides a digital read out of the trucks voltage at all times with the key on. See attached link:
KM29 Pro Bluetooth FM Transmitter | Nulaxy
Everything on these new trucks require the proper voltage and AMPS to work correctly. So, it is imperative to know the correct voltage and not rely on idiot gages that the automotive manufactures are now putting in these trucks.