Yup, despite the fact that his only possible connection to India would be some kind of colonial history in his family, the extremely white Cumberbatch played Khan. Naturally, a lot of people called the movie out for casting a white actor who also never once attempted to proudly display his glistening man-cleavage.
But rather than leave this kinda racist thread hanging in the middle of Star Trek's continuity, the comic book tie-in stepped up to the plate and addressed the pasty white elephant in the room. The series Star Trek: Khan takes place immediately after the events of Into Darkness, with Khan on trial for all of his evil dickishness. We then see flashbacks to Khan's past, when he looks like a combination of Montalban and, you know, an actual Indian person.
With a tiny bit of our aunt thrown in (specifically, the hairdo).