Add the chicken, carrots, celery, potatoes, tomatoes, green onion, water, garlic oil, curry powder, salt, pepper, and ginger to the Instant Pot. Stir well and then place the lid on. Hit the "manual" button and set the time to 10 minutes.
Once done cooking, let natural release for 5 minutes then release the pressure by hitting the "cancel" button and sliding the valve to release the pressure.
Remove the chicken to a cutting board and add in the coconut milk to the soup mixture.
Blend the soup mixture a little with an immersion blender. Just a little to add creaminess, but leaving chunks. This step is optional, but makes for a much creamier soup. Hit the "sauté" button and let mixture cook a little while you chop the chicken.
Chop up the chicken and add back to the soup mixture. Hit "cancel" and serve warm.