Placing the tstat probe inside the tub is incorrect and places your animal in harm. If the probe gets moved the tstat will run hot and could burn your snake as well as cause other issues. The only probe that should be put inside the tub is one of a thermometer.
Op, Have you put something in the tub that could represent the snake laying on the tub floor over the heat tape? This will make the tub lay on the heat mat and should raise the surface temp.
If so it is common to run the tstat at a higher temp to give the desired hotspot temp inside the cage do to heat loss because of the distance travelled through the materials of the cage.
Any substrate over the hotspot needs to be thin, 1/4 is usually good.