This is my villa. I have villas all over the world, and I allow Cynthia to use them. You are welcome to come and play whenever you wish.""Tell me something. Are you familiar with Battle Castles? You can find them in Johto and Sinnoh, so challenge them to improve yourself.""I used to own Battle Castles. Then I became one of Unova's Elite Four. Will I be a Champion somewhere next? You never know!""Darach is as neat as always. He came all the way to Unova, cleaned the villa, and then went home...""Having no psychic powers at all is better than having psychic powers you can't control."
This suggests that they are either roommates or Caitlyn is Cynthia's real estate agent. Or they're great friends.
"Having everything go your way is the road to disillusionment. Knowing the difference between what's impossible and what's possible... I used to know someone who talked about that a lot. No matter how hard I try, I cannot defeat Cynthia. Before, I would have exploded with rage. Now, I have the tranquility to reflect on my performance to see how I can improve.""Tell me something. Are you familiar with Battle Castles? You can find them in Johto and Sinnoh, so challenge them to improve yourself.
Implying that they've batted in the past and their constant rematch obviously shows that they've build a connection that way.
Even here Caitlyn "expects" Cynthia to bring such a strong Pokémon to the battle. Later Cynthia states "You've grown my dear Caitlyn". That too supports the past two quotes, despite being from the game. Caitlyn concludes my theory with"My heart skips a beat every time we battle."
Hopefully, I've Helped!