They’re not US citizens.
They have no direct rights under our Constitution.
Um, wrong.
Aliens in the U.S. have essentially the same rights as citizens for many purposes because of the 5th and 14th Amendments’ language, but aliens do not have constitutional rights against the U.S. government outside its territory.
Once detained in the US, they have the right to petition for a writ of habeas corpus available to them to appear before a judge or court.