In a bowl, combine the sugar, vinegar, cumin, dill, turmeric and red pepper flakes and stir together until the sugar is dissolved. Add the cucumbers, shallots and olive oil. Toss well and season to taste with salt and pepper.
Prepare a grill for cooking over medium heat.
Grill the turkey sausages until seared on both sides and cooked through, about 10 minutes per side. Brush the naan with some oil and sprinkle with cumin and turmeric on one side to add color. Grill , turning once, until warmed, 1 to 2 minutes total.
Spread each naan with 1/2 tablespoon sour cream, if desired, and top with some of the cucumber relish. Top with the grilled sausages. Serve extra cucumber relish on the side.