Place whole chicken in Instant Pot breast side up. Then add water, Adobo, and black pepper. Lock lid, close vent, and set cook for 30 minutes at high pressure.
Meanwhile - Place onions is food processor (with blade attachment) and pulse a few times, until coarsely chopped. Add tomatoes, red bell pepper, cilantro, garlic, and capers to food processor and pulse just until fully combined. (Should make about 2 cups.)
Once cook time is complete, allow pressure to release naturally (will take about 30 minutes). Then transfer chicken from pot to a separate bowl. Be careful because it might be falling apart, which is good!
Pass broth through a fine mesh strainer and return to pressure cooker.
Add tomato/cilantro mixture, Sazón Goya, olives, and rice to broth and mix well. Lock lid and cook at high pressure for 3 minutes. Once cook time is complete, quick-release pressure and remove lid.
Meanwhile - separate all chicken meat from bones in bite-sized pieces. Discard skin and bones.
Add chicken to pot and mix well. Serve and enjoy!