why did the authors of the constitution include the proviso "or a Citizen of the United States, at the time of the Adoption of this Constitution," into article II, section I, clause 5?
Let's let Supreme Court Joseph Story answer that question:
It was doubtless introduced (for it has now become by lapse of time merely nominal, and will soon become wholly extinct) out of respect to those distinguished revolutionary patriots, who were born in a foreign land, and yet had entitled themselves to high honours in their adopted country. A positive exclusion of them from the office would have been unjust to their merits, and painful to their sensibilities.
So, with this understanding, we can see what a NBC is not-It is not someone born in a foreign land or else there would have been no need to introduce the provision.
Don’t bother wasting everyone’s time, including yours and mine, by lecturing me on the obvious and already well understood Constitutional provisions.