ORAS is technically Gen 6... how do you get a Sylveon in ORAS? Are Fairies released at all in this game? I'm confused...
You can capture Eevee on Route 116 in ORAS after capturing/defeating Kyogre/Groudon (Note that Eevee is a "hidden Pokémon", which means you probably need to find it via DexNav). To evolve it into Sylveon, make sure it knows a Fairy-type move (like Baby-Doll Eyes) and just raise its affection to 2 hearts in Pokémon Amie.
Another way to get Sylveon into ORAS is by trading it from XY to ORAS.
Yes you go to the Pokemon amie and get 2 affection with an eevee that knows a fairy type move and then you level it up 1 lvl