Cut 4 6-inch rounds out of the pie crusts, and fit them into 4 5-inch mini pie dishes. Cut remaining pie crust into 1/8-inch strips, and set dough aside.
In a bowl, mix the diced apple, tapioca, sugar, lemon juice, nutmeg, and cinnamon until thoroughly combined; allow the mixture to stand for 5 minutes to soften the tapioca. Stir the mixture again, and spoon into the pie shells. Use the strips of dough to weave a small lattice crust on top of each pie, and pinch the strips onto the bottom crust.
Bake in the preheated oven until the pies are browned and the filling is thickened and bubbling, about 30 minutes. Cool before serving.