Remove phyllo shells from freezer 15 minutes before using. Reserve a small amount of whipped topping for garnish. Combine remaining whipped topping with pumpkin; mix until smooth. Mix in pudding mix until fully combined. Pour filling into a plastic zip-top bag; seal and cut off a small corner. Pipe pumpkin filling into the phyllo shells. Divide the reserved whipped topping over tarts; pipe out of another zip-top bag if desired. Sprinkle pumpkin pie spice on top.