Nobody. But US military facilities are considered US soil and thus US jurisdiction.
In the SCOTUS rulings on Guantanamo, SCOTUS went further and stated that they would have ruled the same way if it had been a CIA facility instead of a military facility, so long as Cuba had granted the CIA permission to exclusively use the land for its own purposes.
In the SCOTUS rulings on Guantanamo, SCOTUS went further and stated that they would have ruled the same way if it had been a CIA facility instead of a military facility, so long as Cuba had granted the CIA permission to exclusively use the land for its own purposes.