Preheat the oven to 350 degrees F (175 degrees C). Coat a 12-cup fluted tube pan with nonstick spray. Place a piece of rolled-up foil into the tube part of the pan to prevent cake from spilling over the top. Pour caramel topping into the prepared pan.

Beat cake mix, water, 3 eggs, and vegetable oil together in a large bowl until well combined; pour evenly over caramel topping.

Combine condensed milk, evaporated milk, 4 eggs, cream cheese, and vanilla in a blender. Process until smooth; pour slowly over cake batter. While baking, the cake will rise and the milk mixture will go to the bottom.

Coat a piece of foil with nonstick spray. Cover the pan tightly with foil, coated-side down. Place the pan in a large roasting pan. Pour hot water into the roasting pan to a depth of 2 inches.

Bake in the preheated oven until a toothpick inserted in the center comes out with a few moist crumbs on it, about 2 hours.

Place cake on a cooling rack; cool for 15 minutes. Remove foil and invert onto a serving plate. Cool for 1 hour at room temperature. Chill for 4 hours or overnight before serving.