>Recruiting Pokémon is very different in this game to the predecessors. Rather than there being a slim chance of them wanting to join you after you have defeated them, this time the recruiting is tied in with Connection Orbs. If you have connected with the Pokémon, then you can use it in dungeons away from the main story. This is available after Ampharos gives you your first Connection Orb.
Yes, the Connection Orb missions have replaced the old ways of recruiting. Also, you can only recruit one of each species/evolution line (RIP team of four Sableye).