Put the chicken, half of the green jalapeno, half of the garlic, the allspice, 1/4 teaspoon salt, and pepper to taste in a large bowl. Mix with your hands and form into four 1/2-inch-thick oval patties. Put the patties on a plate, cover and refrigerate until ready to cook.
Heat 1 tablespoon vegetable oil in a large skillet over medium heat. Add half of the red onion, the remaining green jalapeno and garlic, and the turmeric and cook 1 minute. Add the rice, 1/4 teaspoon salt and 2 cups water. Bring to a boil, stir and reduce the heat to medium low; cover and simmer until the rice is tender, about 15 minutes. Add the peas but don't stir; cover and set aside.
Heat 1 tablespoon vegetable oil in a nonstick skillet over medium-high heat. Add the patties and cook until firm, about 4 minutes per side. Toss the pineapple, cilantro, red jalapeno, and the remaining red onion and 1/2 tablespoon vegetable oil in a bowl. Season with salt.
Stir the rice and peas and season with salt and pepper. Serve with the patties and pineapple salsa.