Heat oil in a large deep skillet over medium-high heat. Sprinkle 3 teaspoons of cajun spice mix all over the chicken on both sides and transfer to the heated skillet. Cook until golden brown on both sides and cooked through, 3 to 4 minutes a side. Transfer cooked chicken to a cutting board and let rest while you make the pasta.

Reduce heat to medium. Add onion and garlic to the same skillet and cook, stirring, until softened, about 3-4 minutes.

Add the uncooked pasta, milk and broth. Season with the remaining cajun seasoning and salt. Bring to a gentle simmer and cook, stirring often until pasta is al dente and liquid is absorbed and creamy, 12 to 15 minutes.

Slice the chicken and transfer it on top of the pasta along with the chopped tomatoes and chopped green onions.