As near as I can tell, you're setting Z0 to the wrong place in Mach. In Aspire, you've specified that Z0 is the center of the part (which is generally the appropriate thing to do in rotary work). In Mach, you also have to set Z0 to the center of the part, not to anything related to the surface. Your note seems to indicate that you've set Z0 to something else, related to the diameter of the part. It needs to be set to the exact center (both in Z and in X) of your rotary axis.
As I mentioned, In Aspire, in the Wrapped Job Setup, the Center of the XY origin is chosen and the bottom of the Cylinder axis is chosen (which is really the middle of the cylinder being machined). Since you can't or don't want to drill a hole to the middle of the cylinder, the mill is placed on the top of the cylinder and half the material thickness is starting point (in the positive) and that number tells Mach 3 where the mill is. Also, I failed to mention, in the Material Setup, the Safe Z should be 1/2 the material thickness Plus an additional amount to clear the cylinder once the spindle retracts. The G-Code tells Mach 3 the diameter. Nothing else needs to be set.
Sometime I work in Aspire in inches, but my machine is setup in millimeters. When I save the post processor, Aspire will automatic convert it to the millimeter. If you notice the material setup is inches, however in Mach 3, it shows millimeters.