That is a very good point! Gravity is just such an ingrained intuition that people tend to be ok with saying things go into the spacetime wells, but it is a little tautological.
My understanding is that a more correct intuition is thinking of straight paths on the curved sheet. Say it's like a loosely woven tablecloth - objects in free fall will go along the threads of the weave, so if you stretch the fabric by placing a heavy object on it, the paths of smaller objects on the fabric will be stretched towards the heavy thing.
This metaphor falls apart for orbits though, as it requires "stretching" the fabric so much that the threads now somehow go in a circle around the mass heh. But the underlying principle is the same - an object in orbit is in free fall along a straight path in curved spacetime.