Read it again. Jurisdiction as it meant at the time was that they were not subject to jurisdiction from any other government.
...as for foreigners not being subject to jurisdiction of the United States, our government has always had extradition treaties with other countries that include crimes committed here. So no, not everyone here is subject to the original intended jurisdiction of the United States, including EVERY illegal alien, and many are not subject to the newer Leftist derivation of jurisdiction, depending on what extradition treaties the United States has with their country of origin.
Nimrata Randhawa was born to two non-citizens and was not subject to the jurisdiction of the United States until her parents became citizens. They could have left with her at any time before then if they wanted and the United States had no jurisdiction to say otherwise.
Your interpretation is a common mistake.
People conflate the civil rights act of 1866 with the 14th amendment.
The civil rights act of 1866 granted citizenship to “all persons born in the United States and not subject to any foreign power”. That language would have the effect that you are talking about. However it was changed in the 14th amendment to read “subject to the jurisdiction thereof”.
So it wasn’t that the meaning of “jurisdiction” was different at that time. It was that in 1866 the law read “not subject to any foreign power” and in 1868 the Constitution was changed to read “subject to the jurisdiction” instead.
The use of the term “jurisdiction” is to exclude diplomats, ambassadors and such. Their children are not US citizens even if they are born in the US.