In my view, and for a properly designed foundation, such movement should be kept by design to serviceable levels, for the practice is to detension when the basement floors are built and then able to take the inwards forces.
The structural scheme must be valid both under the original tie system and the new, bridging between the new support at basement floor levels. Since these use to be quite close, the span for the inwards push is small and so feasible to sustain high push with reasonable basement walls.
So for construction as described movement should be minimal, and designed to be so.