If an illegal alien commits a murder in the U.S., he can be prosecuted. If a foreign diplomat commits a murder in the U.S., he cannot be prosecuted because he has diplomatic immunity. Illegal aliens are therefore subject to our jurisdiction.
All aliens are subject to the laws of the country in which they are physically present. However, they are also subject to the jurisdiction of the country of their citizenship. They not only must obey the laws of their location, but those of their country. That is inherent in every nation's sovereignty.
The 14th amendment's use of “jurisdiction” is well documented to be synonymous with “allegiance”. It was written that way, it was considered that way, and it was ratified that way.
Citizenship based solely on place of birth was part of monarchies. Basically; “You were born here. You belong to me.” We rejected that concept with the Revolution and the War of 1812. United States citizenship comes from the parents citizenship or naturalization, not place of birth.