Preheat oven to 350 degrees. Prepare a muffin tin by greasing with nonstick cooking spray. Cut each sheet of puff pastry into nine equal squares.
Place each square inside a muffin cup and press into the cup. Bake the pastry cups for 10 minutes. When the pastry begins to brown, remove from oven and allow to rest for five minutes.
While the pastry is baking, make the apple pie filling by adding cubed apples, lemon juice, and water to a medium saucepan.
Bring the mixture to a simmer and cook for eight minutes.
In a small bowl, combine the brown sugar, cornstarch, cinnamon, allspice, ginger, nutmeg, and salt. Add the mixture to the apples and stir to coat. Simmer for two minutes then remove from heat and allow to cool slightly.
Use a spoon to press down the center of each pastry cup, then fill the cup with apple filling. Top the apples with chopped pecans. Place the pies back in the oven and bake for 5 to 10 more minutes, or until the pastry is golden brown.
Allow pies to cool for five to 10 minutes in the pan, then remove to wire rack to cool completely before serving.