Bring a large pot of lightly salted water to a boil; cook rotini at a boil until tender yet firm to the bite, about 8 minutes. Drain and keep warm.
While the pasta is cooking, melt 2 tablespoons butter in a skillet over medium heat. Add figs and saute in melted butter until browned, 3 to 5 minutes. Add balsamic vinegar, chicken stock, honey, and thyme; bring to a simmer. Simmer until sauce begins to thicken, about 3 minutes. Lower heat and keep warm.
Meanwhile, season salmon with salt and pepper. Melt 1 tablespoon butter in a skillet over medium-high heat. Add salmon and sear both sides in the hot skillet. Reduce heat to medium and cook until fish flakes easily with a fork, about 7 minutes.
Divide pasta between two plates. Top with salmon fillets and pour equal amounts of reduction over each dish.