First, can you get an image of the problem?
What size is the dry mount tissue in relation to the print? Could it be smaller than the print causing the edge?
What is the platen size?
What is the mat size?
What is the mat brand?
Could it be the print paper? Have you tried this with another type of paper/mat combination?
What is the temperature of the press and how long do you press the image?
Again, to understand correctly, you have the heat platen on top of 2 4 ply mats, the print, the tissue, and then the mount board?