An inside stairway and wall are to be built some time later than the foundation walls of a house. Their footings will be built at the same time as the footings for the foundation walls. Will these inside footings be enough to keep the stairway and internal wall from settling independently?
They may not settle independently, but to be sure they don't, and to restrain any possibility of lateral movement, you should cast dowel rods into the external walls to provide adequate connections.