Ideally you are not using your thumb to apply pressure.
Using the thumb and fingers in opposition to squeeze the string down onto the fingerboard tightens up the whole hand, leads to premature fatigue, and can lead to more serious injury. In my case I ended up with tendonitis in the left elbow and a perpetually sore thumb joint, until I learned to change the way I stop the notes.
You really can apply enough pressure for good tone by using the shoulder and arm to apply force through the hand and fingers into the strings to contact the fingerboard.
I don't claim to be able to totally disassociate my thumb from the process, but there are those who claim to be able to completely remove the thumb from contact with the neck.
You might find more in the Orchestra Technique section.