To be sure it is clear what Vattel is saying here, I have quoted another passage from his Law of Nations
The citizens are the members of the civil society: bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. The natives, or natural-born citizens, are those born in the country, of parents who are citizens. As the society cannot exist and perpetuate itself otherwise than by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights.The society is supposed to desire this, in consequence of what it owes to its own preservation; and it is presumed, as matter of course, that each citizen, on entering into society, reserves to his children the right of becoming members of it. The country of the fathers is therefore that of the children; and these become true citizens merely by their tacit consent. We shall soon see, whether, on their coming to the years of discretion, they may renounce their right, and what they owe to the society in which they were born. I say, that, in order to be of the country, it is necessry that a person be born of a father who is a citizen; for if he is born there of a foreigner, it will be only the place of his birth, and not his country.
A natural born Citizen must be born in the nation of his father's citizenship to be a natural born Citizen. This appears to mean that being born in a land foreign to your father gives you less than natural born Citzen status. This can result in dual citizenship subject to laws of naturalization.