Drain pineapple and mango in a fine mesh strainer fitted over a bowl. Transfer pineapple and mango to a large bowl; mix in bananas and lime juice.
Mix sugar, tapioca, cinnamon, ginger, and salt in a separate bowl. Add sugar mixture to fruit mixture; toss to coat. Fold in butter pieces. Set aside until flavors have blended, 15 to 30 minutes. The longer it sits, the better it will set up during baking.
Press 1 pie crust into a 9-inch plate plate; spoon fruit mixture into pie crust. Top with the second pie crust, crimping the edges together to seal. Cut a few slits in the top crust for ventilation during baking. Line the crust edges with aluminum foil to prevent burning.
Bake in the preheated oven for 25 minutes. Remove aluminum foil and bake until crust is golden brown, 20 to 25 minutes. Cool completely on a wire rack.
