They have the right to due process once they cross. In the case of illegal border crossings, the process is well-established.
The US Border Patrol catches someone crossing illegally and puts them on a bus. That bus takes them back to Mexico. Process complete, and perfectly legal.
Thanks for playing, migrants!
I think I read that most of them waive due process and just accept the bus or plane ticket home instead of having to sit in a cell to wait for their case to be settled.
They have absolutely no US rights until they're at the border.