First, put a bucket underneath the discharge pipe of the T&P valve to determine if the water is coming from there. If it is, then go to one of the big box stores or a plumbing or hardware store and pick up a water pressure gauge with a tattle tale hand (to show peak pressure) and put it on someplace where it will fit (WM supply, hose bib, drain of the WH, etc.). Leave it overnight, or longer if possible. See what the pressure is 'normally', and what the peak reading is while hooked up. If it exceeds 150# (give or take a little), that's why the safety valve is opening.
If you have a closed system (either a check valve or a pressure reduction valve), expansion of the water in the WH will raise the pressure enough to cause this safety valve to open and dump a little water. The pressure gauge will show you this. If you have a PRV and DON'T have an expansion tank, you need to have one installed. If you DO have an expansion tank and a PRV, the PRV OR the expansion tank may be bad, allowing the pressure to rise enough to trip the safety valve. A new tank, especially if it is larger than the old, will be more efficient and may have more water that can expand when heated, and it may show the problem where it wasn't exhibited previously.
If it is leaking from the tank and not the T&P valve, the plumber is likely to cover it since many have a 1-year warranty, and the tank has a longer one.