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This looks mechanical… It looks very much like the mug is drifting on the rotary… what I’m thinking of only occurs on a wheel or roller type rotary.
Is this a roller (wheeled) or chuck type rotary?
There is clearly a gap going vertically on the mug… Check that nothing is adhered to the pulleys… this bump in the belt during a run can generate that type of anomaly.

If you’re plugged into the Y axes, lowering the jump-off speed and the acceleration to very low values… single digits… will help
The mug is probably moving right to left as it rotates… Hopefully the lower acceleration will help… but you may have to fiddle with how the rotary hangs onto things… It’s pretty common that these have a tendency to slip randomly.
Save the current configuration and save the rotary configuration once setup…
You can re-load which ever one you need without issue…