ALT + S is used to scale geometry along the normal, if it behaves like this when you press ALT + S it's because your normals are facing that way.
I don't know what is the tutorial and I don't know what you did differently compared to it but normally if you have a circle, the normals of each vertex should be pointing to the center of the circle so even when you delete half of the circle, you should still probably have this when you extrude and do ALT + S :
So the best solution for you would be to start over, create a new circle and delete half of it but if, for some reason, you can't redo everything from the beginning, you can do the following :
Select the two vertices at both end of your half circle
Press SHIFT + S choose
Cursor to Selected :
it will snap your cursor at the center of your circle. Then, change the pivot point to 3D cursor :
Then, press E then S to scale the vertices and it will scale them according to the 3D cursor :