Heat the oil in a pressure cooker over medium-high heat or use the brown function. Add the chicken, sausage, and shrimp.
Sprinkle the meats with half the Creole seasoning, half the thyme, and half the cayenne. Sauté for 3 to 5 minutes uncovered, stirring frequently, until chicken and shrimp are thoroughly cooked. Remove chicken, sausage, and shrimp with a slotted spoon and set aside.
Add the onion, garlic, bell pepper, celery, and remaining Creole seasoning, thyme and cayenne to pressure cooker. Sauté 4 to 5 minutes, stirring frequently until vegetables are crisp-tender.
Add the rice, tomatoes with their juice, and stock. Secure the cover and bring to high pressure. Cook for 8 minutes. Release the pressure, remove the lid, then stir in the chicken, sausage, shrimp, and parsley. Cover tightly and let stand 5 minutes before serving.