I seriously doubt that more than a few of them gave it any thought at all. There were big issues at stake - control over the money (many of our founders were terrified because states under the Confederation were allowing the use of "paper" money), slavery, the slave trade, the proper counting of slaves for purposes of allocating House seats, how to protect small states from big states, the limits of Congressional power, separation of powers, war and peace, treaty powers, interstate commerce). As to the selection of presidents, they clearly expressed their view that the president should not be selected directly by the people, but only by electors (who were to be chosen in the manner specified by state legislatures and who were thus expected to be a bit more predictable) than the rabble.
The drafters did not provide the kind of specific and precise definition that will answer your question (by birth, at birth or something else) with certainty. That could be because they viewed it as a minor matter (at what point in the future would it even become relevant given the exception?) compared to other issues that were far more problematic and pressing. Or, it could be that they didn't feel there would be any consensus if definitions were proposed. It could even be because they really didn't care exactly how electors might deal with nuances and just assumed that decisions by electors would fall within an acceptable range of definitions. The founders stopped writing when they stopped writing. They were drafting a Constitution. It can't be read like a mortgage.
By the way, who were the founders? The guys who met in Philadelphia and voted to send their document to the states? How about the ones who voted no in PHiladelphia? Were the folks who met in state conventions founders, too? How about the ones who voted against ratification? The Constitution begins, "We, the people . . ." Was everyone a founder?
How many of those folks spent any time thinking about the question you've raised? How many had ever heard of Vattel? How many were tossing around the Latin terms you can find in these threads?
The Constitution is very clear about who is to select the president. The founders provided electors with the eligibility requirements that the founders wanted to give them. Each of those electors is required to apply those Constitutional standards. Just like Supreme Court justices, they might not all answer your specific question in exactly the same way, but they are all bound by the same standard.
First, I don't think the Framers of the Constitution - or just as importantly, those who voted to ratify it - thought about the term very much at all.
To the extent that they DID think about it, they would have thought about it in terms of what "natural born citizen" meant to them, either popularly or in a legal sense.
I think popularly, it meant what it means now: "born a citizen."
Legally, it meant the same thing as "natural born subject" had always meant, except that now we were "citizens," not "subjects."
In neither case did it necessarily require two citizen parents. And I would say that in neither case did it necessarily require being born on US soil, either.
As to how many of the Framers and Founders and ratifiers of the Constitution had read Vattel: Damn few.
And as to how many of the Framers and Founders and ratifiers of the Constitution gave Vattel any weight at all in the meaning of the term "natural born citizen:"
ZERO.