[Cyropaedia]

Wrong. It is possible to be born here and "not subject to the jurisdiction thereof". Both criteria have to be met. That is why they wrote down both clauses. They weren't just talking about the children of Ambassadors, for example.

They citizenship clause deals with persons "born" (or "naturalized") and "subject to the jurisdiction thereof". Thus, being born here does not confer automatic citizenship.

[Michael Michael]

Wrong. It is possible to be born here and "not subject to the jurisdiction thereof".

Yes. If you were born to an ambassador or other diplomat, or, at the time, to an Indian. Then you were not subject to the jurisdiction thereof. Otherwise, you were indeed subject to the jurisdiction thereof.

They weren't just talking about the children of Ambassadors, for example.

Again, there is no conjunction anywhere in that phrase. The "foreigners, aliens" being referred to were those children born to ambassadors and other diplomats.