Rotary settings…get flat image at the start

Check the preview first to make sure the paths are being generated as you expect, if it looks good, then it could be backlash in the rotary axis, or slipping of the roller.

Try adding a very small filled shape eg. 5mm x 1mm high just below the edge that doesn’t cut straight away (cut at 0% power), this will ensure that the axis is primed against backlash by having it pre-driven in the same direction that the job will start in;

If that trick helps, you will need to check the rotary mechanism for any slop.

If it is just slipping on the roller, clean the surface of the driving roller, try putting a couple of rubber bands on your cup it may help it to grip better.

Also, temporarily halving the acceleration of your rotary axis ($121) may also help.