I'm assuming that this is not a power vent type heater, just a run of the mill type.
A picture would likely help. The questions are where is the water actually coming from and when? Is it coming from the stack? Is it coming from the T&P relief valve? Is it coming from a water line connection? Or is it coming from inside the central flue or combustion chamber of the water heater?
Why is water being allowed to stand in the catch pan at a level that is getting the water heater wet? Doesn't sound like a good installation to me.
My first guess is that this is actually a thermal expansion issue. Is the T&P set up to overflow into the pan? If so, then it is easy to determine if it is leaking. If it isn't leaking constantly then check to see if it is relieving because of pressure spikes due to thermal expansion. It would be best to put a ~$10 test guage (with a max pressure indicator) on a hose bib during testing and overnight. All you need to do to see if it is relieving during thermal expansion is to do a long hot water draw such as filling a tub, then allow the water heater to recover. While the tank is in heating mode the pressure will rise and if there is not some sort of thermal expansion tank or other relief, it will hit about ~150 psig and the T&P valve will start dribbling excess volume. If you see this, the issue is that a thermal expansion tank is needed (or that an existing one has failed or needs its air pre-charge reset.)
Hearing this described as "condensating" is a red flag to me if it is coming from the plumber's description. It is not a normal technical term and might be an indication that the plumber is a bit weak on understanding...or not. If you are in SW Texas I assume you are across the dry line and don't have much humid air. As such this would make condensation in the stack itself less likely. To get that you need warm humid air to be coming into contact with cold walls in the stack. With double wall stacks and the heater running this is unlikely. Some sort of air infiltration or backdraft might cause some drip down the stack. This is more typical on the outside of uninsulated AC ducts running through humid unconditioned spaces.
Condensation on the chimney/combustion chamber walls will happen when tank gas water heater is cold and is first fired up, but it only last a few minutes. This can be observed through the flame inspection window--I've seen this. Water can drip down on the burner and make the flame turn yellow until the tank walls warm enough that the condensing stops. One would have to be running the tank really cold and doing full draws regularly to accumulate water in the pan this way.