Why is my Water Heater Leaking only when I open the Pressure valve?
Check the age of the tank.  The lining is most likely leaking.  The pressure vent doing what it is suppose to do,  When you manual release the pressure through that valve, water is allowed to escape.  The real leak is in the lining, and dripping down to the bottom of the tank.  If the bottom is above your drain pan, you should be able to water dripping from the bottom of the tank.
Replacing the relief valve is not going to fix the leak.  It was leaking before you touch the relief valve.