I have never used that device. How long you ask? That's a tough one.
Taste the wine before you start stirring to get an idea of the taste of CO2. It is sort of bitter and you can feel it on your tongue, like the sparkle in sparkling wine.
Stir for about 30 seconds, then stop. You will see small bubbles coming up the sides of the carboy. Give the bubbles time to come to the surface, then repeat until you don't see the bubbles anymore.
Taste the wine to see if it tastes CO2 free. Fill a small wine bottle about half full of the wine. Shake it really well. If you get a large 'puff' of gas when you open it, it still has CO2, so repeat stirring. Also, you will get tiny bubbles, like you see from pouring a coke, if there is still CO2.
Bare in mind that you can put plain water in a bottle and shake it and get some bubbles (larger bubbles, though) and even a small 'puff' of gas. You have to experiment to learn to tell the difference between this and what the presence of CO2 does.