Turn on a multi-functional pressure cooker (such as Instant Pot) and select Saute function. Melt butter and cook onions until soft and translucent, about 3 minutes. Add garlic and saute for 30 seconds. Stir in tomatoes, tomato sauce, and chipotle peppers. Mix in chicken and stir to combine. Close and lock the lid.
Select high pressure according to manufacturer's instructions; set timer for 12 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Season with chili powder, cumin, and salt. Serve on top of tostadas with toppings of your choice.