Position a rack in the lower third of the oven and preheat to 450° or preheat a grill over medium. In a small bowl, mix the hot sauce, allspice, jerk seasoning and nutmeg with the finely chopped scallions and 1 tbsp. ginger.
Place the chicken on a rimmed baking sheet. Spoon 1 tbsp. scallion mixture under the skin of each chicken thigh; spread the remaining scallion mixture all over the chicken. Bake, basting once withthe pan drippings, or grill until cooked through, about 10 minutes per side.
In a medium bowl, mix the pineapple, lime juice and jalapeños with the sliced scallions and remaining 1 1/2 tsp. ginger; season. Serve the chicken with the pineapple salsa and lime wedges.