The key term and phrase of the above is: "and (subject to jurisdiction thereof)"
In the case of Kamala's parents (who lied on official documents to gain and hold their student visas) this claimed application of the law requires clarification by the courts.
Please examine the available link and documents, as this is discussion of substance with very serious implications.
Also in October 1964 US births to persons who were 50% of India parentage, were subject to the quota of the 1952 Mc Carran Walter Act (which limited India to 100 immigrants per year).
Kamala's birth certificate evidences her mother's action to evade that immigration limitation.
The documents and language are quite clear. Please consider those facts.