Actually, even changing the duplicate selection offset to be a multiple of the snapping distance, trying to align the duplicate with the original wouldn't be fixed if I understand correctly what you're doing.

As of now the snapping to the grid is with respect to the bounds of the objects, and not made to make relative displacements be multiples of the grid size (could be a second mode for the snapping).

Though in this case using a multiple of the grid size for the offset when duplicating works in both case (duplicated object still snapped for both definitions) so it makes sense to add this in the code