Cook the linguine in salted boiling water until al dente. Save 1/2 cup pasta water, then drain.
Pat the chicken dry and season with 2 teaspoons Cajun seasoning, smoked paprika, garlic powder, and black pepper.
Heat olive oil in a large skillet over medium-high heat. Sear the chicken in batches for 6 to 8 minutes, turning occasionally, until golden brown with lightly crispy edges and cooked through to 165°F. Add 1 tablespoon butter and 3 minced garlic cloves during the last 30 seconds, tossing until the chicken is coated in fragrant garlic butter. Transfer to a plate.
In another skillet, melt the remaining 2 tablespoons butter over medium-low heat. Add the remaining garlic and cook for 30 seconds. Pour in heavy cream, then stir in the drained diced tomatoes with green chilies and remaining Cajun seasoning. Simmer gently for 3 minutes.
Reduce the heat to low and gradually stir in Parmesan and mozzarella until melted into a smooth, creamy cheese sauce. Add the cooked linguine and toss until every strand is generously coated. Stir in a little reserved pasta water if needed. Taste and adjust the salt.
Spoon the creamy cheesy Rotel linguine onto one side of each plate and arrange the golden Cajun garlic butter chicken bites beside it. Drizzle any remaining garlic butter over the chicken and finish both portions with freshly chopped parsley.