No, you don't receive them at checkin. Or at least we didn't. But any time during your stay you just go to the place(s) at your resort that sells and fills the mugs and "purchase" them there. Just be sure to tell the person at checkout that you're using the plan to pay for them. You will get a receipt that says $0.00.
Except some resorts don't have food courts. For instance at Y&BC, you can go to Hurricane Hannah's, BC Marketplace (the closest to a food court but it isn't) or Beaches and Cream.