When discussing whether the Constitution follows the flag, people tend to conceptualize the question as whether or not the Constitution applies overseas. But is that the proper question? While the Supreme Court may have initially conceptualized the question that way in In re Ross, where it held that the Constitution cannot have effect in another country, in every other case since Ross, the question has been formulated more in the frame of "Who has the right to enforce the Constitution overseas?"
The first time this formulation appeared was in the United States v. Curtiss-Wright Export Corp., 299 U.S. 304 (1936). There, the Court wrote that "Neither the Constitution nor the laws passed in pursuance of it have any force in foreign territory unless in respect of our own citizens." 299 U.S. at 318. This formulation indicates that, if a U.S. citizen is involved, the Constitution would apply.
The Court echoed this formulation in Reid v. Covert, where the question was whether the Sixth Amendment applied to American citizens overseas, accompanying U.S. military forces. Relying on the citizenship of the military spouses, the Court said yes. And this formulation also played a role in United States v. Verdugo-Urquidez, which focused less on whether the Fourth Amendment applied in Mexico, and more on whether Verdugo-Urquidez had the right to claim the protections of the Fourth Amendment. Indistinquishing Reid, the Court noted that it dealt with citizens, rather than aliens. Furthermore, the implication of the Verdugo-Urquidez majority's holding is that, had Verdugo-Urquidez possessed substantial connections, the Fourth Amendment would have applied.
Thus, it appears that the better way to conceptualize the extraterritorial application of the Constitution is to start with a presumption that the Constitution does apply anywhere that the U.S. Government acts, but that there is a limited group of people who have standing to enforce its provisions, if those acts take place outside the United States. I'll dive into this more in future posts.