Where are you getting that definition from? Subject to jurisdiction simply means being subject to the laws of that nation. Other than diplomats and a few other unusual exceptions, everyone in the US is subject to this country's laws.
Why do I have to show you this???
Secretary of State Bayard ruled under Section 1992 of U.S. Revised Statutes in 1885 that although Richard Greisser was born in the United States, his father at the time of his birth was a subject of Germany, and thus, Richard Greisser could not be a citizen of the United States. Furthermore, it was held his father was not subject to the jurisdiction of the United States under the Fourteenth Amendment.
The constitutional requirement for the President of the United States to be a natural-born citizen had one purpose according to St. George Tucker:
That provision in the constitution which requires that the president shall be a native-born citizen (unless he were a citizen of the United States when the constitution was adopted,) is a happy means of security against foreign influence, which, wherever it is capable of being exerted, is to he dreaded more than the plague. The admission of foreigners into our councils, consequently, cannot be too much guarded against; their total exclusion from a station to which foreign nations have been accustomed to, attach ideas of sovereign power, sacredness of character, and hereditary right, is a measure of the most consummate policy and wisdom. … The title of king, prince, emperor, or czar, without the smallest addition to his powers, would have rendered him a member of the fraternity of crowned heads: their common cause has more than once threatened the desolation of Europe. To have added a member to this sacred family in America, would have invited and perpetuated among us all the evils of Pandora’s Box.
Additionally, Charles Pinckney in 1800 said the presidential eligibility clause was designed “to insure … attachment to the country.”
What better way to insure attachment to the country then to require the President to have inherited his American citizenship through his American father and not through a foreign father. Any child can be born anywhere in the country and removed by their father to be raised in his native country. The risks would be for the child the return in later life to reside in this country bringing with him foreign influences and intrigues.
Therefore, we can say with confidence that a natural-born citizen of the United States means those persons born whose father the United States already has an established jurisdiction over, i.e., born to father’s who are themselves citizens of the United States. A person who had been born under a double allegiance cannot be said to be a natural-born citizen of the United States because such status is not recognized (only in fiction of law). A child born to an American mother and alien father could be said to be a citizen of the United States by some affirmative act of law but never entitled to be a natural-born citizen because through laws of nature the child inherits the condition of their father.