This is definitely not normal....My guess is that the old water heater valve did not do this...you either have bad luck with NEW pressure relief valves, which I doubt, or your water pressure sound too high and is above the relief pressure of the valve. Ask your city water department if the pressure is abnormal...and certainly the plumber should have none what is normal on pressure. Then check with the hot water heater manufacturer or check the manual that came with it and see if you can tell what pressure the relief valve should relieve pressure at.--I personally have never seen or heard of this problem on a new hot water heater!!!
More helpful info at this site as well http://www.chilipepperapp.com/troubleg.htm
good luck and hope this helps....let us know what your problem turned out to be also..by posting back up.