Yes you do - the trophy states you must find them in one sitting. And yes, you get spirits for the pairs you find, but when the candle resets, letting you play again, the board resets, all the spirits hidden once more.
As for the rest of the games, I already note down the spirits. I tried doing it for the dark candle before realising that when the candle resets, the spirits all move so it was a waste of my time.