I read the passages, again, in the U.S. Constitution, and the Declaration of Independence. They are crystal clear, and I could detect no penumbras or permutations. I guess I’m not SCOTUS material.
If you wish to argue from a spirit or intent of the law vs letter of the law, then I can agree with your position. Otherwise, words have meaning, and the meaning of jurisdiction and allegiance in the context used in the material I’ve already cited is clear.
Too bad you have no idea what an idiom is. An idiom is more than the sum of its parts. You can take each word out and determine its meaning separately yet misunderstand the meaning of the idiom. It seems you have only a desire to understand a particular word and not the meaning in the setting it is used.
Go ahead hold on to your own interpretation and forget about the true meaning if you wish. I’m sure the meaning of that word in the Declaration and in other parts of the Constitution is clear. But then they did not use the term “subject to the jurisdiction thereof” now did they. Find that exact phrase of that idiom elsewhere in either of the two documents you mentioned then look at the meaning. If you can’t find the idiom, you won’t find the same meaning.
If you don’t understand something, do a little work. The meaning is clear, but not if you attempt to read your own interpretation into a phrase without understanding.
I’m not going to do this for you. The meaning, history, and background is available to everyone. This is your opportunity to learn something. I’d take it if I were you.