Hi Pierre,
The change axis problem is present even in the tutorial. If you repeat the video between 3:25 and 3:31 you will notice it. This problem is present in the automatic wheels creat with expresso even in some car rigs offered for sale on the Internet, but the effect of this does not appear during the animation except with careful examination, because you will not select the wheel so the axis will not expose us. However, if this bothers you, you can move the wheel manually by calculating the distance and the wheel diameter. I have placed a screen recording below explaining the method.
I hope this is useful to you.