I recently read some posts along the same lines suggesting that the optical centre is not aligned with the mechanical centre of the objective lens on cheaper scopes. This results in the POI describing a circle as the objective lens is rotated for parallax adjustment.
I just accept it as a lesson learned about cheap scopes and re-zero if I adjust the parallax.
I also have a Hawke Sport HD (HK series) 4-12x50 which is not a PA scope but was easily adjusted on the objective lens to suit airgun ranges. This is certainly adequate for my needs, as the depth of field at the magnifications that I favour provide a sharp image with a consistent POI. The parallax error is now minimal.
I will avoid choosing a PA scope in future unless I am prepared to spend a substantial sum and get a side focus rather than an objective bell adjustment.