Subject to the jurisdiction of means having to obey the law of the United States. Everyone in the USA, citizens and aliens (both legal and illegal) has to obey the laws of the USA. Only foreign diplomats and their families do not, and they are the only ones in the USA that are not subject to the jurisdiction.<quoted text>Sorry, I don't use de Vattel, to controversial. The 14th was nothing more than the Civil Rights Act of 1866, placed into the Constitution as an amendment.
"Subject to the jurisdiction,thereof" simply means, "not subject to any foreign power".
Who does not know that every person born within the limits of the Republic is, in the language of the Constitution, a natural-born citizen. Rep. John A. Bingham, The congressional globe, Volume 61, Part 2. pg. 2212 (1869)