How can an illegal immigrant have Constitutional Rights in America, when they are not a U.S. citizen?

Until the day i retired, i never understood why our District Attorney sent a letter to each department, advising us that each illegal immigrant we arrested, for an unrelated crime, had to be advised of their Constitutional Rights. how can undocumented people have Constitutional Rights, if they are not citizens of the United States? did someone forget they are here illegally? if i visit Mexico, i have to have documentation for their country, so why is this only working one way? is the state of Arizona on the right track? if suspected illegal immigrants are not documented, then they are violating the law. how do the police know and how can they tell, if they don’t ask??? (maybe this is what the feds had in mind all along. to keep it undercover).