Combine chicken thighs, olive oil, ground cumin, paprika, turmeric, garlic powder, salt, and black pepper in a bowl; toss to coat. Marinate at room temperature for at least 15 minutes (or cover and refrigerate up to 4 hours).
Rinse basmati rice under cold water until water runs clear. In a saucepan, melt butter over medium heat; add rice and salt, stirring 1 minute. Pour in chicken broth (or water), bring to a boil; reduce heat to low, cover, and simmer 15–18 minutes until liquid is absorbed. Remove from heat and let rest, covered, 5–10 minutes, then fluff with a fork.
In a bowl, whisk mayonnaise, Greek yogurt, white vinegar, lemon juice, minced garlic, sugar, and salt until smooth. Add water 1 tablespoon at a time until sauce is pourable.
Heat a skillet over medium-high heat. Add marinated chicken in a single layer (in batches if needed). Cook 5–7 minutes, stirring occasionally, until browned and cooked through (165°F/74°C internal). Remove from heat.
Divide rice among plates. Top with spiced chicken, shredded iceberg lettuce, and diced tomatoes. Drizzle with white sauce and serve with hot sauce to taste.