Anyone who was a "citizen" of the United States at the time of ratification (1789) was eligible to become President.
That would make children eligible, and immigrants since Independence who became citizens of a state would be grandfathered in, making their future children also eligible.
It would not include British soldiers who deserted, French or German (Hessian) soldiers who remained, etc.
-PJ
do you have a reference for immigrants being grandfathered in after 1789.
Side bar: Here is Madison responding to a petition from a candidate claiming his opponent was not a citizen for7 years in 1789.
So far as we can judge by the laws of Carolina, and the practice and decision of that state, the principles I have adduced are supported; and I must own that I feel myself at liberty to decide, that Mr. Smith was a citizen at the declaration of independence, a citizen at the time of his election, and consequently entitled to a seat in this legislature.