Take the probe and put it on the surface of the mat not between the glass. Use metal tape to secure down the edges of the mat. Tape the probe (not on the tip but on the cord) to the mat and place styrofoam between the mat and the table or item the tank is on. This keeps the probe secure and in contact with the mat and insulates the bottom of the tank if you put styrofoam across the entire bottom of the tank. You don't have to have the probe between the mat and the glass with those stick on heat mats because it can do exactly what you are having issues with. On the surface in the middle of the mat is just fine.
I do this for my rosy boa cage and use styrofoam under all my enclosures. You can get styrofoam sheets are hardware stores like lowes or home depot.