Combine water, kosher salt, and sugar in a saucepan over low heat; cook until sugar and salt dissolve, 4 to 5 minutes. Set aside to cool to room temperature.
Score the skin side of each piece of chicken 2 to 3 times, about 1/8 inch deep. Place chicken pieces in a large bowl or lidded container.
Puree cherry tomatoes, habanero peppers, garlic, and allspice with the salt and sugar mixture in a blender until smooth.
Pour tomato brine over chicken pieces, making sure all pieces are covered. Refrigerate 4 to 6 hours.
Remove chicken pieces and transfer to a plate or baking sheet lined with paper towels. Pat chicken pieces dry with more paper towels.
Preheat an outdoor grill for high heat and lightly oil the grate.
Combine thyme, cumin, black pepper, cayenne pepper, and oil in a small bowl.
Brush each chicken piece with thyme and oil mixture.
Cook chicken, skin side down, on the preheated grill for 1 to 2 minutes. Turn each piece and move to indirect heat. Cook until well-browned and meat is no longer pink in the center, 30 to 35 minutes. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).
Brush each piece with Thai sweet chile sauce. Transfer to a plate and allow chicken to rest for 10 minutes before serving.