Set Instant Pot to Sauté and add 1 tablespoon neutral oil to pot. Carefully swirl Instant Pot to coat bottom with oil then let pot heat up.
Once oil is hot and shimmering, add andouille sausage slices to pot. Cook 3 minutes, then carefully flip sausage rounds over and cook another 3 minutes or until sausage rounds are golden brown on all sides. Transfer sausage pieces to bowl or plate and set aside.
Add 1 tablespoon oil to Instant Pot. When oil is hot, add chicken pieces and cook chicken 2 to 3 minutes. Carefully flip chicken pieces over and cook 2 to 3 minutes more or until chicken is browned on all sides. Transfer chicken to bowl or plate and set aside.
Add remaining 2 tablespoon of neutral oil to Instant Pot, when oil is hot, add chopped onion, bell peppers, celery, and garlic. Sauté veggies, stirring occasionally, until onion is translucent - approximately 3 minutes.
When onions are translucent, stir in Cajun seasoning, black pepper, salt, cayenne pepper, and uncooked rice. Stir 1 minute or so, until rice is fully coated with spices.
Press Cancel button to turn off heat, then stir in diced tomatoes and chicken broth.
Once ingredients are combined, secure lid on Instant Pot with valve in sealing position. Set to Manual High Pressure for 8 minutes. Once Instant Pot pressurizes, cook time will begin.
When 8-minute cook time ends, immediately Quick Release steam and carefully remove lid. Add shrimp, sausage, and chicken to Instant Pot and stir to incorporate proteins into rice mixture.
Secure lid on Instant Pot and let Instant Pot sit 5 to 10 minutes, until residual heat has cooked shrimp fully. Once shrimp is cooked through, portion jambalaya into serving bowls and serve immediately.