You are right to be concerned regarding the possibility of your rifle’s zero shifting from one magnification setting to another. This can be a common problem and is one that many shooters forget to check when they purchase a scope. It is usually the cheaper scopes that suffer from this displacement problem.
I test a scope’s repeatability by setting a target at 30 yards for a rimfire rifle and at 100 yards for a full-bore, and then shoot a three-shot group at each magnification setting to ascertain if all the shots fall at the initial point of impact.
A small degree of shift is acceptable, and for you to decide, but at longer range it could be the difference between a hit and a miss or, worse, a wounded beast.
It is worth spending more money on a quality scope, or stick to a fixed-power scope that will obviously not suffer from this problem.