Varys was recruiting Dorne and the Reach to Daenarys' side.
There is a similar dialogue in A Feast for Crows between Prince Doran Martell and his daughter Arianne (who does not appear in the show):
[Arianne] narrowed her eyes. “What is our heart’s desire?” [Prince Doran]“Vengeance.” His voice was soft, as if he were afraid that someone might be listening. “Justice.” Prince Doran pressed the onyx dragon into her palm with his swollen, gouty fingers, and whispered, “Fire and blood.”
This conversation serves the same purpose as the show conversation, to announce that Dorne is finally coming into the conflict, and they are supporting the TargeryensTargaryens.
Characters in universe would understand that Varys/Prince Doran are referring to the Targaryens, because "Fire and Blood" is their house words.
In the final scene, you are able to see a ship with the Dornish sigil sailing in the fleet. (Right side of the image)
We can assume that Varys' meeting in Dorne occurred well before the final scene showing the fleet leave Meereen.
Asynchronous storytelling is a common tool in Game of Thrones and explains most of the timing discrepancies that we see.