the threaded ring of the DG2 that screws into the eyepiece is actually designed to rotate independent of the magnifier. As such, the magnifier itself can be rotated even when the threaded ring is screwed into the R-D1 eye piece tightly.
In other words, yes.. the unit will swivel left and right even when installed properly and tightly. For me, the DG2 would hit a part of the camera preventing me from tightening it. So the technique to tighten the eye piece would be to swivel the whole unit in the direction of tightening. Then use my fingers to hold the DG-2's threaded ring in one place. Then swivel the DG2 back to the left. Then hold the DG2 and its threaded ring as a single unit and turn to the right further tightening the unit to the R-D1 eye piece. Continue this "ratcheting" motion until the DG-2's threaded ring is tightened on the RD-1. The DG2 will still swivel left and right BUT it should not do so freely... It should have some resistance.
There is also a circular spring inside that locks the magnifier in the down position. Its locks into place too strongly and difficult to swing away quickly. So I took a pair of pliers and removed it.
I intended to use the magnifier to help with critical focus on fast 50mm lenses BUT its 2x magnification is too much. The 50mm frame lines are no longer visible requiring me to focus with the DG2 down and flip it up to recompose. As such, its usefulness was limited. I later found the field of view of the magnifier roughly approximates a 90mm focal length. So it found a new purpose with 90mm lenses.