Preheat Instant Pot to saute setting. Add milk, cream cheese, and butter. Cook, whisking to incorporate, until cream cheese is melted and mixture has come to a simmer. Add cheddar, gruyere, garlic, and cayenne. Whisk until smooth and season generously with salt and pepper. Add pasta, fold to combine, and place top on Instant pot.
Set pressure to high and cook for 6 minutes. Release pressure manually and open lid. Adjust seasoning with additional salt, pepper, and cayenne. If desired, thin with additional ¼ cup milk. Serve immediately, garnished with chopped chives and cayenne.