Depending on your weight and overall activities, you should see a significant increase in your daily burn, but not 400-500 calories unless you are very large or start moving more based on feeling an increase in energy. 

The mixture of caffeine, other related compounds and the Green Tea extract EGCG in Fat Burn 3 has been shown to stimulate between a 10%-15% increase in metabolism. 

Therefore, if you normally burn 2000 calories a day and you start using Fat Burn 3, you may see an increase to 2200 calories per day.  If you don't actually see the increase on your web program it's due to the fact that the increase in body heat is too small to be detected by the sensors on the armband (but the increase is there).  Fat Burn 3 not only works to increase your metabolism but also leads people to increase their spontaneous physical activities (e.g. instead of sitting around, you feel more energetic and therefore move more), which of course the bodybugg will pick up.  This combination may be what led your gym to conclude that a 400-500 calorie increase may be possible.