1) You must apply the transformed segment both to the "Bottom side" and "Y Evenly" slots. In your scene, only one of them has offset.
2) The segment uses "Deform->Apply Box Mapping", so the mapping coordinates of the reference object are ignored.
3) I agree that segment mapping needs some additional controls. But using a separate material for the Back 1 segment, with Mapping->Coordinates->Angle W = 90º should work fine.