In a large bowl, combine the chicken pieces, yogurt, and 1 tablespoon of the tikka masala spice mix. Allow to marinate for at least 30 minutes (or up to overnight in the refrigerator for best results).
Heat the vegetable oil in a large skillet or pan over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Add the minced garlic and grated ginger to the pan, cooking for another minute until fragrant.
Stir in the diced bell pepper and sauté for an additional 3-4 minutes until it's slightly softened.
Add the marinated chicken to the pan, folding it into the mixture. Cook until the chicken is browned on the outside, about 6-7 minutes.
Add the canned diced tomatoes, coconut milk, remaining tikka masala, turmeric, and cumin powder. Stir well to combine.
Bring the mixture to a simmer and reduce the heat to low. Cover the pan and let it cook for 15-20 minutes, or until the chicken is cooked through and tender.
Season with salt and pepper to taste, adjusting spices as needed.
Once cooked, remove from heat and garnish with fresh cilantro. Serve hot with cooked basmati rice or warm naan bread.