No, Vattel didn’t define NBC that way. He didn’t use the term, but instead used “indigenes” and “natives”. It took a bad translation made AFTER the US Constitution to insert that.
"Les naturels, ou indigenes, sont ceux qui sont nes dans le pays, de parens citoyens"
He used the word "Citoyen", which is the word we still use, rather than the English "Subject."
How did we switch? Why did we switch?
Could it be that when we abandoned "Subject", with all it's "perpetual allegiance" connotations, we embraced the source of law that uses the term "Citizen"?
"Citizen" is barely referenced in English Law of that era, and it did not utilize the meaning we use today.