I found another engine part, found the center with the bullseye, used the L bracket and put the cutter in the bracket.
This time however, I only gently put the cutter on the paper (loosen the pressure on the blade a bit too) and adjusted the arm so the tip of the blade was right on the edge of the part.
Lock the blade in place and adjust the pressure back. Time to cut! How will I do?
Looks perfect to me, and no hole poked in the middle! This is why I wanted to try this tool, and it works great.