To make the jam, heat oil in a saucepan over medium heat. Once hot, add onions and jalapenos, cooking until softened, about 6 minutes. Stir in rum and cook until almost all of the liquid has evaporated. Stir in pineapple, lime juice, and sugar. Bring to a simmer and cook for about 10 minutes until softened. Remove from heat, then stir in cilantro, salt, and pepper. Set aside.
Preheat grill. Once the grill is hot, add carne asada to the grill. Grill until medium rare, about 2 minutes per side.
Let meat rest for 10 minutes. Slice into thin strips.
Spread halved buns with butter. Top bottom halves of the buns with slices of carne asada, dividing evenly between the buns.
Top with cheese and place on a sheet pan. Place sheet pan in the oven with the broiler set to High. Broil until cheese is melted, about 1 minute.
Top sliders with slices of tomato and avocado. Finish with a heaping tablespoon of pineapple jalapeno jam. Finish with the top halves of the buns.
Serve immediately.