I think it’s generally well established that rights travel abroad with citizens. However, it’s less clear if they apply abroad (or even to U.S. territories) to non-citizens. E.g. United States v. Verdugo-Urquidez claims it does not apply to non-citizens who do not have a voluntary association with the U.S.

Edit: I'll try to be more clear. The rights of U.S. citizens extend beyond the border when dealing with the U.S. government. I was not implying other governments must recognize U.S. Constitutional rights when dealing with U.S. citizens.