Preheat oven to 375 degrees F (190 degrees C). Place tart shells on a baking sheet.
Beat brown sugar and butter together with an electric mixer until creamy; beat in eggs, corn syrup, vanilla extract, lemon juice, cardamom, cinnamon, nutmeg, and ginger.
Divide raisins evenly into the bottom of tart shells; pour about 2 tablespoons syrup mixture into each tart shell.
Bake in the preheated oven until pastry is golden and filling is set, about 20 minutes; remove to cool on a wire rack.