Sear the sausage: Turn on your Instant Pot to “Sauté” on “Normal” setting. Once it’s hot enough, add sausage and sear for 2 minutes on both sides. Transfer to a plate and set aside.
Sear the shrimp: Add olive oil to the pot. Add peeled shrimp and garlic, and cook for 3 minutes, stirring constantly to avoid burning the garlic. Once cooked, transfer to a plate and set aside.
Sauté the vegetables: Add onion, celery, bell pepper, and tomatoes to the pot. Cook for 5 minutes, stirring constantly. Add Cajun seasoning, thyme, basil, paprika, chili powder, lime juice, Tabasco, salt, and black pepper. Cook and stir for another 5 minutes.
Toast the rice: Add rice to the pot and stir constantly for a couple of minutes to avoid sticking to the bottom of the pot.
Cook the jambalaya: Add chicken broth to the pot. Stir to distribute the rice evenly into the broth. Cover and seal the lid. Turn the venting knob to sealing position. Choose the "rice" cooking setting program and cook for 12 minutes.
Add finishing touches and serve: Carefully turn the venting knob to release steam. Open the lid and add cooked sausage, shrimp, and freshly chopped scallions. Mix everything together. Transfer the jambalaya to a plate or bowl and serve.