Trim excess fat from the chicken and cut into 1‑inch cubes.
Heat the olive oil in a large skillet over medium heat. Add the chicken and diced onion and cook, stirring occasionally, until the chicken is cooked through, about 6–8 minutes.
During the last minute of cooking, add the minced garlic and cook until fragrant, about 1 minute. Remove the chicken and set aside.
Reduce heat to low and pour 1 cup of the milk into the skillet. Whisk in the flour until smooth to form a roux.
Slowly whisk in the remaining milk and the chicken broth, keeping the sauce smooth.
Add the salt and black pepper, bring the mixture to a gentle boil over medium heat, and cook until slightly thickened, whisking frequently.
Stir in the can of mild Rotel and the uncooked angel hair pasta. Increase heat to high to bring the mixture to a boil, then reduce to medium‑low, cover, and cook 8–10 minutes, stirring occasionally, until the pasta is al dente.
Add the cream cheese pieces and shredded Mexican cheese to the skillet and stir until melted and creamy.
Return the cooked chicken to the skillet, stir to combine, and heat through.
Garnish with the diced, seeded tomato if using and serve hot.