The soot that's getting on your smoked meat could be coming directly from the smoldering wood, or more likely, it's the buildup on the inner surface of the smoker lid flaking off and falling onto the meat.
It's normal for smoke and grease vapor to combine inside smokers and accumulate on the inner surfaces of smokers. As the layer of gunk thickens, it becomes prone to flake off. This isn't much of a problem when the sooty buildup falls off the sides of the smoker, but when it falls from the underside of the lid, it lands on the meat.
It's not necessary to clean the inside of your smoker after every use, but an occasional cleaning is a good idea, especially of the smoker lid. Use hot water, dishsoap and some elbow grease to remove the grunge. Use a dishcloth or plastic scrubber pad. Refrain from using anything abrasive. You'll be able to smoke several times before the lid needs cleaned again.