Kinki EX-1 Volume Knob

It's likely it uses a digital attenuator controlled by both the remote electronics and the volume control. So, not necessary for volume to move every time.

Could someone please tell me if the volume knob should also rotate when using the volume on the remote control?

no it does not

(i am assuming you are referring to the kinki ex-m1 or m1+ integrated amps)

I just checked my ex-m1+ and it does not.  

Thank you!  Noromance  & Carlsbad