When a Border Patrol tower went up in their New York backyard, they wondered what it could see, and who exactly was watching.

Catalina “Xochitl” Santiago, who came to the U.S. at 8 and is legally in the U.S. through the Deferred Action for Childhood Arrivals program, or DACA.

Alvaro Castro Velasquez, 19, was to graduate with his class on June 27. Instead, he was in a detention facility on the other ...