You don't add the dining plan to tickets, you add it to a room reservation package. Tickets must also be purchased as a part of that package unless you are in one of the three categories exempt from the ticket purchase requirement: annual passholders, military room discount, or DVC members booking through member services.
So if you already have purchased tickets from a third party, you would likely need to purchase more tickets to make your reservation a package - it would require at least 1 day tickets per person (2 days for the free dining promotion).