Thanks for the case. Kawakita v. US, 343 U.S. 717 (1952)
My question was aimed at finding the reach of "under the jurisdiction." The example I hypothesized was what I'll call a "nominal citizen," that being a person born on US soil, who at a young age departs the US and resides with his alien parents in an alien land, and other than for being born, is not in the US at the time a draft or other "call for citizens" is made.
Kawakita is quite a different critter from that, as one can discern by reading the case. I don't think finding Kawakita to be a US citizen is a stretch, as he seems to obtain that status by acts that resemble naturalization (oaths of allegiance), even if he has US citizen status at birth (which he would, being post WKA).
Also of interest in the case, are citations to the expatriation by operation of various section of the Nationality Act.
Ahhh, found this, which I think answers my initial question:
"A person with dual nationality may be subjected to taxes by both states of which he is a national. He is not entitled to protection by one of the two states of which he is a national while in the territorial jurisdiction of the other. Either state not at war with the other may insist on military service when the person is present within its territory. In time of war if he supports neither belligerent, both may be aggrieved. If he supports one belligerent, the other may be aggrieved. One state may be suspicious of his loyalty to it and subject him to the disabilities of an enemy alien, including sequestration of his property, while the other holds his conduct treasonable." Orfield, The Legal Effects of Dual Nationality, 17 Geo. Wash. L. Rev. 427, 429.
And so, "subject to the jurisdiction" is clearly not some fixed quantum - and too, a dual citizen born in the US is not amenable to the draft, unless present on US soil.
Kawakita is a darn good example of the risk in finding a dual citizen at birth to also be a "natural born citizen" for purposes of qualification for the presidency.
U.S. Constitutional law and statutory law still to this day do not recognize a right of dual citizenship. The U.S. Supreme Court has entered some arguably contradictory decisions which have had the effect of denying Federal and state governments the ability to enforce some laws affecting individuals exercising de facto dual citizenship privileges in some cases. The U.S. State Department, however, continues to warn that persons who claim dual or multiple citizenships may in some events be unable to avow themselves some protections otherwise due to a person claiming U.S. citizenship and a foreign citizenship/s at the same time.
It depends on the country with whom the dual national shares nationality. Some countries do have agreements that have been codified in particular treaties that shield or insulate its citizen from conscription unless they're on US soil. But, absent those agreements - and there are not very many - Americans who enjoy dual citizenship are required by law to register for selective service (and therefor are subject to conscription), irrespective of their actual residence.
Also, many people don't realize that individuals between the ages of 18-25, who are legal alien residents MUST register with the Selective Service, or face penalties up to and including deportation, FWI