You've draw a shape layer. Shapes in a shape layer have their own position and anchor points, which are separate from the layer's position and anchor points.
Best to expand them both, and set the shape's positions to the centre of your comp, then you can adjust the layer's position.
Would you mind sharing the tutorial link so that we can understand what's happening?
Not sure if it'll help but you can try moving the Anchor point to the center of the shape. Navigate to Layer > Transform > Center Anchor Point in Layer Content or use the shortcut Ctrl + Alt + Home.
It is a paid tutorial you have to login to view it. Only thing is I can upload a video of the instant. I wish to know the duration of a video that is allowed in this forum.