True. The founders were born subjects of the King but considered themselves to be natural born citizens of their respective States hence the language in the Constitution.
"Citizen" was brought to America by Emerrich de Vattel. English people didn't use the word much, but the founders reading Vattel is why Americans started using the word "Citizen."
It was always "Subject" prior to "Droit des Gens" arriving in America.
If we were following "Common Law", we would have stuck with "Subject", but what many people today want to do is combine the framework of "Subject" with the usage of the word "Citizen", and it is an unnatural fit.