Latios is not exclusive to Omega Ruby. I know, because I've got Alpha Sapphire and I have both Lati Twins. I caught them legitimately in-game; I did not trade Latios over from another game; and I did not cheat to get him.
In my experience with Alpha Sapphire, you have to get an Eon Ticket. Talk to your father, Norman, once you do—he'll take you to a ship which sails you to the place where Latios awaited in my game. I assume it is the same with Omega Ruby, except that rather than Latios being there it will be Latias.
Anyway, to answer your question, I have always had Latias answer my summons when I played the Eon Flute. I don't know whether it is just programmed like that, or something, but that's what happens to me. I presume it is similar in its counterpart game.