I've used the Canon equivalent, called Auto Focus Micro Adjustment, for several years. If the Nikon Auto Focus Fine Tuning is anything like Canon's version you have two choices when performing AF Fine Tune: calibrate for a specific lens or calibrate for all lenses. If all of your lenses require a calibration in the same direction then you should adjust the camera (all lens adjustment) to the middle of that range. Then reduce the individual adjustment for each lens the same amount in the opposite direction and fine tune each lens again.

If your camera's registration distance (image plane to flange distance) is accurate, then any back focusing error should be proportional. That is, if the lens back focuses by 20cm at 6m, then it should be expected to back focus by about 6-7cm when focused at 2m. In terms of a percentage of the depth of field, this is the same error since depth of field will be 3x wider when focused to 6m than when focused to 2m. Most calibration tools recommend using a distance of 25-50x the focal length of the lens, which would be 1.25-2.5m for a 50mm lens.

Unfortunately, the theory doesn't always work that way because lens designs are often a compromise between competing factors. In general, with prime lenses you will probably get the best results if you adjust the lens to the distance halfway between the shortest and longest ranges you frequently use. If you most often use the 50mm lens between 2m and 6m, then calibrate it for 4m and see if that works well enough at both distances. If not, then a trip to a Nikon Service Center might be needed to calibrate the lens to your camera.