Cut off the tops of the apples.
Using a paring knife, cut out shapes to make jack o' lantern faces.
Using a melon baller, scoop out the inside of the apples, leaving at least 1/8-inch of apple flesh on the sides and 1/4-inch on the bottom. If you scoop out more, the apple cider will drain through the jack o' lantern face.
Squeeze lemon juice over apples to prevent from browning and set aside.
Combine apple juice, orange juice, caramel topping, cinnamon, and allspice in a large saucepan.
Cook over medium heat and bring to a boil, stirring occasionally.
Remove from heat, stir in the rum, and pour into the apple cups.
Garnish with cinnamon sticks.