There are two ways to advertise on cable TV — buy ads on the networks, or buy ads through the cable companies. In either case, you can specify programs or pay less and have your ads scattered throughout the day.
I’m not the least bit surprised that the Army Reserve — or any branch of the military — would advertise on MTV, because the 18-24 demographic is their target, and MTV gets those eyeballs. Whether they specifically chose that program or not, I don’t and can’t know.
They have to be aware of the shows that they are advertising on. I can’t imagine you would see a commercial for the Marines while a show like ‘Queer Eye’ is airing. It wouldn’t make any sense.