The cylinder absolutely should NOT rotate when it is closed in the frame with the hammer & trigger at rest. In this mode the cylinder stop should be locked into the cylinder notch of the 6 o'clock chamber to prevent rotation either way. Sounds like your cylinder stop is either worn or stuck in the partially retracted position.
If the gun does not appear to have been fired a lot then the cylinder stop may just be gunked up with dried up oil. Locate it in the bottom of the frame cylinder window. It's a little half-moon piece of shiny steel. Press it down with your finger to see if it retracts and then pops back up under spring compression when you release pressure on it. It should return briskly with no sign of sluggishness. Squirt some penetrating oil in there if it's not coming all the way back up (or returns sluggishly) and work it until it appears to pop up with gusto.
A worn cylinder stop can also allow the cylinder to over-index when fired in double-action mode, meaning the cylinder will rotate more than 1/6 of a turn but less than 1/3 of a turn with the result that the firing pin falls somewhere between two cartridges. No bang. You'll usually see firing pin strikes on the rim with this condition.
I had this over-indexing problem with a Model 14-2 that I owned. I bought a cylinder stop from Numrich and that solved the problem but you have to take most of the internal parts out to get to it. I did not experience the reverse rotation problem you describe, but it's definitely not normal operation. Good luck.
-Lee
