When I ordered my set-up, I told Dave the weight range of bullets I wanted to make, and I supplied him with samples of the tubing I planned to use. Some of the "finshed product" he sent back to me had folds in it as well.
Each of the punches supplied by him were marked with the length of the piece of tubing to be used with them, so I couldn't cut them all wrong, could I :? ? However, my set being for flat-based bullets meant I wasn't supplied with a separate end-flattening punch, but was required to use my core-seating punch. Maybe this could have been a factor.
I tried deeper and lesser anneals to see if the folds could be eliminated in that way, but I had no success. I think this is the norm with tubing jackets of this or greater thicknesses. If the tubing was thinner, it might have made thinner and less noticable folds.