Then how can space-time expand over time?
Do you not mean to say 'How can space expand over time?'
If we use the above analogy. The sphere is space-time. It doesn't expand, its just a sphere, remaining the same 'size'. If we start at South the 'circle' we reside at is 0 radius, as we begin to travel north the circle we reside at 'expands'.
I think that's what is being driven at, but I'm aware that a analogy failing can occur without my knowing it: I hope the experts will correct me if I'm wrong.