Assuming a tonearm is unconstrained in the lateral plain during cueing (everything level, dust- and dirt-free, low friction bearings in good shape and properly adjusted, tonearm wire twist and other lateral forces eliminated, little friction between armtube and cueing support), then any amount of anti-skating applied during cueing will move the arm outward. That's what anti-skating devices do, push or pull the arm outward.
Actual behavior varies from one arm design to another. For example, outward cueing drift is typical with Rega arms and their clones, because (1) the anti-skate device applies some force even if set to "zero" and (2) that force is always on. OTOH, cueing drift on a TriPlanar is avoidable. Aside from the option of making anti-skate truly "zero", the anti-skate device is readily adjusted so that outward force is not applied until the stylus touches down.
Other designs may vary in other ways. Check all the factors posted above. If all seems okay then investigate the anti-skating functioning of your arm. Its design may or may not allow you to mitigate outward cueing drift.