Make the BBQ sauce by combining the ketchup, brown sugar, balsamic vinegar and Worcestershire sauce in a small saucepan. Bring the mixture to a boil over medium heat, stirring occasionally. Lower the heat and simmer the sauce for 15 minutes. Season to taste with freshly ground black pepper.
Rub the salmon filets with olive oil on both sides and season with salt and freshly ground black pepper. Place the salmon fillets, skin side down inside the basket or tray. Air-fry the salmon for 5 minutes.