Turn on a multi-functional pressure cooker (such as Instant Pot(R)). Select Saute function and heat vegetable oil. Add cumin seeds and fennel seeds; cook until sizzling, about 2 minutes. Add onion and ginger; cook until softened, about 2 minutes. Stir in cranberries, orange juice, vinegar, salt, and cayenne pepper. Close and lock the lid. Cook on high pressure function according to manufacturer's instructions; set timer for 8 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, about 10 minutes. Release remaining pressure using the quick-release method, about 5 minutes. Unlock and remove the lid. Select Saute function and stir in brown sugar and orange zest; cook until chutney has slightly thickened, about 7 minutes.