My Illustrator design shows "rich black" but when I send it to my Ricoh Aficio GX e3300n printer the black comes out dark maroon/brown.
That printer has quite comprehensive driver setting guidance. Seemingly Mac driver has much less control than Win driver. See a screenshot of the manual:
If you are Win user, be sure that K is used for black in your image and printer settings.
BTW the proper "rich black" mixture is different for different print processes.