The operative passage from the decision is this: "But it is said that the jurisdiction is complete under the 'laws and usages of war.' It can serve no useful purpose to inquire what those laws and usages are, whence they originated, where found, and on whom they operate; they can never be applied to citizens in states which have upheld the authority of the government, and where the courts are open and their process unobstructed."
Plainly, in areas that did not uphold the authority of the federal government, were in a war zone, and had no operating civil courts, such as Tennessee and those areas that purported to secede; the "laws and usages of war" do apply.
quod erat demonstrandum
Exactly what don't you understand about "at all times and under all circumstances," capitan? There is no qualifier there of any form. No "war zone" exception. No "doctrine of necessity" exception. Nothing. The Constitution is SUPREME over all other authorities, civil or military, and none has the right to shun so much as one word of its text on the whims of convenience.
Nice try, but that part of the case applies to the matter of military versus civil trials of the accused, NOT to whether the Constitution itself applies or not. The Constitution ALWAYS applies "at all times and under all circumstances" period.