The final instructions the Horsemen receive are to go to the park. There they find the card-tree of Lionel Shrike, featuring the King of Spades/Swords.
You need five cards for a Tarot reading. The five cards are in order of appearance: King of Spades/Swords, Lovers, Hermit, High Preistess [sic], Death. - TVTropes
So when they saw the fifth card (they had the four cards delivered to them a year back), they knew the reading was complete. To read, they now needed all five cards together. That's what they were referring to.
The King of Spades/Swords is the card referring to the man with the "idea" - their benefactor. Who taught them magic and made them into the Four Horsemen.