She means the tension is set in the bobbin case when the bobbin is not inside the machine. The bobbin and bobbin case are taken out of the machine and set into the gauge. Once the tension is read and set, the bobbin and case are put back into the machine. I personally don't think this has anything to do with what's going on with your quilt.
I have a few questions: Is the brown fabric a batik? You say this has happened before on other quilts, was it the same longarm quilter? Did you show her those quilts and ask about the problem? Can you post a picture of the problem areas?