For me its a definite no to the mat in the tub, one because it can be dangerous and 2 because its an pain to do.
For the thermostat probe, we used to put the probe in the tub below substrate and simply not stack the tub with substrate but now we've found it works equally as well to put the probe straight on the mat outside the tub. You'll need to alter the thermostat setting though according to the temp IN the tub, not the mat temperature