The prevailing definition in the18 century of jurisdiction of the United States is precisely what it is today. If congress really intended to exclude children of all foreigners, not just diplomats, they would have said so and not used the word jurisdiction.
http://webstersdictionary1828.com/ates.
Who was subject to the jurisdiction of a nation was in every book on public law in the 19th century. In fact, most books cited Justice Marshall on the issue in one of the most famous cases our court has decided on public law which only excluded persons subject to the privilege of extraterritoriality (i.e., ambassadors). For example:
“From the definition of a sovereign state it follows that "the jurisdiction of a nation within its own territory is necessarily exclusive and absolute. It is susceptible of no limitation not imposed by itself. Any restriction upon it deriving validity from any external source would imply a diminution of its sovereignty to the extent of the restriction, and an investment of that sovereignty to the same extent in that power which could impose such restriction.' This jurisdiction extends to all subjects and over all persons within its territorial limits, it matters not whether those persons be native-born, or naturalized citizens, or aliens.” George Breckinridge Davis, Elements of International Law, pg. 54-55 (1884)(quoting Justice Marshall).
"[e]very independent state has full and complete jurisdiction over all persons and things physically situated within its territorial limits, whether those persons and things are permanently or transitorily present.” John Norton Pomeroy, Lectures on International Law in Time of Peace, pg. 202 (1886
“All persons found within the limits of a government, (unless specially excepted by the law of nations,) whether their residence is permanent or temporary, are subject to its jurisdiction; but it may or may not, as it chooses, exercise it in cases of dispute between foreigners.” Henry Halleck, Elements of International Law and Laws of War, pg. 92 (1885).
“One of the fundamental rules of international law is that an independent State has absolute and exclusive jurisdiction over all persons and property within its boundaries.” Freedman Snow, International Law, pg. 31 (1898).
“Territorial jurisdiction attached (with special exceptions) upon all persons either permanently or temporarily resident within the territory while they were within it, but it did not follow them after they had withdrawn from it and when they were living in another independent country.” Sir William Henry Rattigan. Private International Law, pg. 228 (1895).
“All persons found within the limits of a Government (unless specially excepted by the law of nations), whether their residence is permanent or temporary, are subject to its jurisdiction; but it may, or may not, as it chooses, exercise it in cases of dispute between foreigners.” Sir Sherston Baker, First Steps in International Law: Prepared for the Use of Students, pg. 79 (1899)