Subject to the jurisdiction is subject matter specific. One isn't under the laws of citizenship when one breaks the laws of speeding, but all citizens and foreigners are subject to the laws of speeding when driving in the jurisdiction of said laws.
But to put it more plainly, when one travels outside the US, one is “NOT” subject to the citizenship laws of the foreign nation and neither is any foreigner subject to the citizenship laws of the US, even though in both cases, both parties are subject to the local laws that keep peace & order to protect the lives of the persons who are in said society whether they are citizens of said society or not.
I just quoted at length, without comment, from a US Supreme Court opinion, with citation.