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But Madison argued that Congressman Smith's birth in South Carolina is all that mattered, because his place of birth came under the sovereignty of of the United States when the US came into existence.

No event subsequent to his birth extinguished Congressman Smith's citizenship in the sovereign state of South Carolina—which, since he was born there and his parents were citizens of the state, meant he was a subject born of South Carolina.

Madison's argument was that any citizen (natural or not) of South Carolina became a natural US citizen at the moment the US became sovereign over South Carolina, provided allegiance to the US was accepted by that citizen. Not a natural born citizen—because the parents would not have been citizens of the US when the person was born—but nevertheless a citizen by natural law, and not by any official act of naturalization.

Without a naturalization law that made Congressman Smith a citizen, and without his having duly undergone the naturalization process specified by such a law, his citizenship cannot be by means of naturalization, but can only be natural citizenship by the operation of natural law.

Right or wrong, that was Madison's argument. And it applies with equal force and legitimacy to all other citizens of the several States, whether they were at home or abroad at the moment the US came into existence. To be logically consistent, either all who were citizens of any of the several States and didn't reject allegiance to the US when it acquired soveignty over their State were citizens of the US by natural law, or none were. If none were, then all would have needed to be naturalized in order to be citizens.