Sketchup Follow-me tool acting funny

I’m making a marble tic-tac-toe game to practice Sketchup and cutting with my CNC mill.

I’m having an interesting problem. I’m trying to make little cups for the marbles to sit in. I make a circle on the surface, then a circle into the material. I then make the perpendicular circle into a fragment and rotate it around using the Follow-me tool.

For some reason it only gives some of the cup shape. I’m missing the lower portion and some other fragments. Any ideas?

Source: xo5

So I tried to do it by subtracting or adding the object from outside as Paul M suggested. For some reason, in this Sketchup drawing I can’t get the follow-me tool to work at all.