It is a common response when starting/increasing an exercise program for your muscles to retain water. This increase in your lean mass can lead to little change, or even an increase, in the scale even as you are burning fat.
This is not muscle tissue in the sense of the red fibery stuff (hence your trainer's comments), but it is lean mass, and does help your body perform better.
However, muscle and water are considerably denser than fat (check www.dailyspark.com/blog.asp?post=quiz_how_
to see a great photo of this, and typically this will show up as inches lost, even if the scale is being unco-operative.
The tape is often a much better means of tracking your progress than the scale. And if you haven't been measuring yourself to date, have you noticed your clothes fitting better?