Stir tomatoes, onion, garlic, ginger, oil, garam masala, paprika, cumin, turmeric and salt in a 4-quart slow cooker. Add chicken thighs and coat with the sauce.
Cover and cook on low for about 6 hours until the chicken reaches at least 165°F and is tender enough to separate with a fork.
Begin the rice during the final hour: bring rice and 1 1/2 cups water to a boil in a covered saucepan, reduce to low and cook for 40 to 45 minutes until tender, then rest covered for 10 minutes.
Lift chicken out, cut into large pieces and return it to the sauce. Turn off the cooker and let the sauce stop bubbling for 5 minutes.
Whisk yogurt in a bowl with 1/2 cup hot sauce added gradually. Stir the tempered yogurt into the cooker without boiling it again.
Divide rice and chicken sauce among 4 bowls.