Your definition is circular. Your statement reduces to "you're a citizen if you've agreed to be a citizen."
The 14th Ammendment is does not establish a protocol for determining, moment by moment, whether or not someone is a citizen. One does not become a citizen by virtue of coming under US jurisdiction, and then lose citizenship upon exiting--perhaps several times in an afternoon, if one lives very near a national border. From the language, the context of the times, and the preceding logic, it is clear that the question of jurisdiction clearly was meant to be of import at precisely one moment, and only at that moment: the moment of birth.
And the meaning of jurisdiction is also perfectly clear. It's dictionary definition:
The Supreme Court ruled in 1884 against an American Indian named John Elk, who despite being born in Nebraska territory and outside his tribe was not considered a citizen.
The majority opinion of the Court read:
The evident meaning of [the jurisdiction phrase] is not merely subject in some respect or degree to the jurisdiction of the United States, but completely subject to their political jurisdiction, and owing them direct and immediate allegiance. Indians born within the territorial limits of the United States although in a geographical sense born in the United States, are no more born in the United States and subject to the jurisdiction thereof within the meaning of the [Citizenship Clause], than the children of subjects of any foreign government born within the domain of that government
That Court's decision has never been overturned and explained why in 1924 Congress provided legislative relief to American Indians. The Court ruled btw children of illegal aliens are not citizens of this country.