Whisk together yogurt, lemon juice, garam masala, ginger, garlic, and salt.
Add cut chicken to the bowl and toss in the marinade until fully coated. Cover with plastic wrap and marinate in the fridge for at least 45 minutes or up to 24 hours.
Turn device on. To make the curry sauce, set the Instant Pot to "sauté " mode and heat vegetable oil. Sauté chopped onions; about 5 minutes. Stir in minced garlic, and minced ginger. Cook for 1 minute.
Stir in turmeric, garam masala, coriander, cumin, salt, and chili powder. Cook until fragrant; about 1-2 minutes.
Drain canned tomatoes; discard liquid. Stir in tomatoes, and tomato sauce.
Place the lid on top of the instant pot and secure it in place. NOTE: Do not add the chicken. The sauce needs to be cooked separately first.
Set pressure valve nozzle to "sealing". Select "manual" or "pressure cook" mode; set pressure cook time on high-pressure for 5 minutes.Note: Pressure cooker will beep once when it comes to pressure. Next it will count down from 5 minutes to cook. Once done, it will beep. Next, the Instant pot will count the minutes that it sits for and may display as "L minutes". Select "cancel" to turn off device. Allow the pressure valve to "natural-release" for 10 minutes. This means you don't need to turn the pressure valve yet; leave it sealed.
Quick-release pressure after 10 minutes by turning the pressure valve from "seal" to "venting". Once the pressure pin drops, open the lid.
Stir in butter until melted. Stir in half and half. Add the chicken and yogurt marinade to the Instant Pot. Stir to combine.
Secure lid on Instant pot. Turn pressure valve to "sealing". Select "manual" or "pressure cook" mode. Set time to cook for 6 minutes.
After timer goes off, allow the pressure to "naturally-release" for 10 minutes. Turn pressure valve to "venting" to manually release remaining pressure.
Stir chicken tikka masala. Serve over rice or with naan bread. Sprinkle top with chopped cilantro.