Hard to say, without seeing your setup. Could be either that your faders are set up incorrectly in the Generic Remote, or could be that the faders are correct in there, but also sending valid CC# data to the Instrument when a MIDI/Instrument track is record-enabled.
To check for the latter, try one (or both ) of two things…
a) make sure that no MIDI/Instrument track is record/monitor-enabled. Are the faders still controlling more than they should be?
b) temporally switch the input of the Generic Remote to “Not Connected”, and see if the faders are still controlling something when a MIDI or Instrument track is record/monitor-enabled.
If the “doubling” is happening because of the MIDI/Instrument track, then you should try using the track’s Input Transformer to filter out the unwanted CC# data.
If the problem persists when no MIDI/Instrument track is record-enabled, then, you are just going to have to look thoroughly in the Generic Remote, and double-check that there are no conflicts. Btw, do you have more than one Generic Remote active?