Why doesn't the relative wind push the control surface back down
But it does, however, some additional lift at the trailing edge from the downward-deflected trim tab remains and prevents the full return to the earlier position. What the trim tab does to the elevator, the elevator in turn does to the whole aircraft: Changing its pitch attitude.
See it this way: Before, the elevator was flying at its force-free angle. Then the added trim tab deflection changed the local pressure distribution on the elevator (in the case of a downward deflection it adds lift), so the elevator assumes a new equilibrium position. This new position is found when the lift change on the elevator just compensates for the newly added lift by the tab. Of course it must go trailing-edge up now.
Trim tabs (picture source)