The question is, "What would a reasonable person living at the time of ratification have understood these words to mean?" The Constitution, with the phrase "natural-born citizen," was ratified in 1788. de Vattel never used the English phrase "natural-born citizen," for he wrote in French, and not everyone translated "les naturels ou indigènes" as "natural-born citizen."
But the British had long defined the phrase "natural-born subject," and a reasonable person living at the time of ratification was a "natural-born subject" of the British Crown until 1783. He would've used the English common law definition of "natural-born subject" applied to "natural-born citizen," not one way of translating a Swiss legalist's writing that doesn't even contain the phrase "natural-born citizen."