Brushcutters

My family farm owns an H235r brushcutter that was made in the 90's. I started it up for the first time this year, and, because it bogged out immediately after starting, replaced the fuel and cleaned the carburetor thoroughly. It now starts and runs fine, but when I shut it off, I get smoke coming out of the exhaust for at least 45 seconds afterward.

Is this a problem, and if so, what should I focus on when troubleshooting? A definitive answer would be nice; my local Husqvarna dealer charges more per hour than I can afford, and I can work on the engine in my shop at home.