Make the jerk seasoning: In a bowl, mix together the brown sugar, salt, herbs, and spices. Transfer it to a tightly lidded jar. The seasoning will last for up to a year in a tightly sealed container in the pantry.
Make the salmon and vegetables: Preheat the air fryer to 375°F and set the timer for 18 minutes. If using a toaster oven-style air fryer, line the cooking pan with parchment paper.
Place the salmon fillet in the middle of the cooking pan or, if using a basket-style air fryer, in the air frying basket. Arrange the tomatoes and sweet potatoes around the salmon in a single layer.
Sprinkle 2 tablespoons of the jerk seasoning blend evenly over the salmon and vegetables, then drizzle on the olive oil.
Bake the salmon, tomatoes, and sweet potatoes in the preheated air fryer.
When the cooking program ends, use a spatula to portion the salmon into quarters. Transfer the salmon to serving plates along with the tomatoes and sweet potatoes. Serve immediately.