Jurisdiction, in this case, isn't referring to criminal jurisdiction. It's referring to the coverage of US rule of law.

In general, that phrase was designed to exclude people who were in the US, but the US couldn't or wouldn't extend the benefits of citizenship and protection of US law to.

This included at the time of the writing, pretty much only diplomatic corps from other countries, due to diplomatic immunity exempting them from most of the US legal system, Native Americans, for whom the reservation system didn't yet exist and they were treated more like separate vassals or protectorate states, and people in US territory occupied by a hostile power, where obviously the US government wouldn't be able to guarantee rule of US law.

The legal concept of a resident alien didn't really exist yet, so it's unclear if they would be subject to the jurisdiction of the US or not. The SCOTUS is being asked to decide that question this year, so we'll have an answer, one way or another.

(My brother is a law student who just asked this of his Constitutional Law professor a month or two ago).