I do not think so it is normal, because in this case you should adjust parallax each time you touch your mag ring.
After you adjusted your diopter to the crosshair for your eye, and then looking through your scope to exactly the same distance (object) at different magnifications with parallax adjustment correctly set, image should stay clear and sharp with sharp reticle as well, no matter which magnification you are using.
Beware of fact that in low magnifications like 5x, 7x etc. the parallax adjustment is not so critical and sensitive to your eye (image stay clear and bright with focused reticle even if there is a small parallax error - simply your eye is not capable to differentiate it), but if you crank you magnification to higher rates like 15x, 20x, 35x, the parallax error pop up more significant to your eye because of magnification. So if you want clear and sharp image with focussed reticle (no parallax) through all your magnification range (for example 7-35x), you should adjust parallax error at the highest magnification - 35x. Once you set it right, there will be no more parallax error through whole mag range in your scope at this specific distance - object.
If your image or reticle goes fuzzy when you cranked up / down your mag ring, you have not adjusted properly:
1) diopter to your eye (reticle does not stay sharp to the image edges)
2) parallax to particular distance - object you are observing
3) your scope has not been properly adjusted / assembled at factory, so you can not remove its error by adjusting diopter / parallax