And after that Venice ceded the island to them. These things have to happen formally regardless of the actual conquest, otherwise the war could not be ended, and the Ottomans would be mere occupiers.
The fact that they ceded it combined with the large payments suggests the Venetians were in no state to continue opposing the Ottomans. They won the battle at Lepanto, but lost the war.
i was just making it clear that the island wasnt just given up