Place all ingredients for the jerk chicken into the insert of an Instant Pot. Set to Manual Pressure on High for 15 minutes. Quick release and use two forks to shred the chicken in the insert.
While the chicken is cooking, make the salsa. Combine mango, red onion, jalapenos, cilantro, lime juice, and black pepper in a small bowl. Stir to combine.
To assemble the sliders, top the bottom halves of the toasted Hawaiian rolls with even amounts of shredded jerk chicken.
Top each slider with a couple of slices of avocado and mango salsa. Finish with the top halves of the buns and serve immediately.