How do potentiometric cells do not proceed through a spontaneous reaction like in a galvanic cell?
First, I wouldn't classify cells as potentiometric or galvanic. 

If you take any electrochemical cell with non-zero total cell potential and connect a wire between the two electrodes it will discharge. This will happen spontaneously in the galvanic direction. 

In potentiometric measurements of electrochemical cells, what you do is a potential measurement which ideally happens at zero current(definition of a voltmeter), and practically at picoampere or lower current. Therefore you are not allowing the electrons to flow from the outside circuit and hence your cell doesn't discharge.