Whisk together 2 tablespoons of the oil, tomato paste, onion, garlic, cumin, cinnamon, allspice, cayenne, and salt and pepper in a large bowl. Add the turkey and parsley and using your hands, gently mix until combined. Cover the mixture and refrigerate for at least 1 hour to allow the flavors meld. Can be made 8 hours in advance and refrigerated.
Heat the grill to high.
Divide the mixture into 12 equal portions and roll into balls. Gently press down on the top of each patty to flatten slightly. Brush the patties on both sides with 2 tablespoons oil and season with salt and pepper.
Grill the kofte until golden brown on both sides and cooked through, about 3 minutes per side.
Whisk together the lemon juice and remaining 2 tablespoons of oil in a large bowl and season with salt and pepper. Add the spinach and toss to lightly coat the leaves in the dressing. Fill each pita with 3 of the patties, top with spinach, red onions and raita. Place a patty Transfer the spinach to a platter and arrange the kofte on top of the leaves. Top each patty with some of the raita.
Stir together the yogurt, apple, salt, cinnamon and cayenne in a small bowl. Cover and refrigerate for at least 30 minutes to allow flavors to meld.