A dispenser box assembly for a laundry appliance that includes a dispenser housing and a lid. The dispenser housing includes one or more housing walls that define a main chamber. The lid is attached to the housing walls and includes an in-lid reservoir. The in-lid reservoir includes an inlet section that is arranged in fluid communication with water inlet ports in the dispenser housing and a diffuser section with an outlet that is arranged in fluid communication with the main chamber. An air port that is open to the atmosphere is arranged in fluid communication with the main chamber such that the main chamber is open to atmospheric pressure and produces a water pressure drop between the water inlet ports and a water outlet port at the bottom of the main chamber.