Heat an instant pot using the BROWN/SAUTE function. Add 1 tablespoon oil and swirl to coat bottom.
Add sausage in a single layer to instant pot and saute 3-5 minutes, turning occasionally until sausage is golden brown. Remove from instant pot and set aside.
Add 1 tablespoon oil to pan and swirl to coat bottom. Add chicken cubes and season with salt and pepper. Saute chicken 3-5 minutes, turning occasionally until chicken is golden-brown. Remove from instant pot and set aside.
Heat remaining 1 tablespoon oil in instant pot. Add onion, pepper, and celery and saute 3-5 minutes until vegetables are crisp-tender. Add garlic, all the spices and rice and cook 2-3 additional minutes until fragrant and rice is lightly toasted.
Turn off BROWN/SAUTE function and add crushed tomatoes, chicken broth, bay leaf, sausage, and chicken to instant pot. Seal instant pot and set vent to closed.
Cook jambalaya on low pressure 12 minutes, then turn off instant pot and allow to release pressure naturally for 5 minutes. Release any remaining pressure in instant pot, remove lid, and use a fork to fish out bay leaf to discard and gently fluff rice.
Season jambalaya with salt to taste if needed and serve warm with green onions on top. Enjoy!