I doubt that it has anything to do with color vs B&W film. I believe the back counts frames only as the roller is turning (since it doesn't count unless you put film/paper in). My guess would be that from lack of use, either the roller or other piece like the clutch was sticking, so you had to wind more for it to register a frame. And possibly by the time you used the second roll, it had seen enough action to run properly. It's just a guess though.
For testing backs and checking frame spacing on 120 cameras, I saved backing paper from 120 films and test wind it through without film. On a roll of paper, I labeled the black side of the paper with the frame numbers 1-12 with a magic marker. So by winding this through and looking through the open shutter at these numbers as I take test exposures, I can see if it's approximately in the right place.
This will usually start to fall behind as I get to the end of the roll, because it's only the paper and not paper+film, so the wind spool diameter is thinner and it doesn't take up quite as much per turn. (Two thicknesses of paper might be about right.) However, it gives an approximate test of whether the camera+back are advancing properly.