new water heater - still leaking from pipe outside of house

Synopsis of this adventure over the last six months:
Water heater is 7 years old.
About 6 months ago, it started leaking out of the "outside pipe" after one of us took a bath.
Changed the T&P valve 3 different times over the last year- it would stop leaking for a few days and then start up again.
Replaced the entire water heater Monday.
STILL LEAKING AFTER WE TAKE A BATH.
What is going on?! I've read up on expansion tanks, and have been told by 3 different plumbers that I don't need one (which is why we bought a brand new water heater). What is the fix? Any ideas?
Oh, and there is ZERO water in the pan in the attic. The only water is coming from this pipe (pictured).

Edit: The pic shows very little water, but the pic was taken at the very beginning. It drips for about 20 minutes.

What is your water pressure normally?

My water pressure is normal & consistent, it doesn't vary. (if you are looking for a number, I dont have that info)

There is no such thing as normal. All water pressure varies. Do you have a water pressure regulator installed? You can go to a big box store and purchase a gauge that attaches to your hose bib, so you will know for yourself. You have two drain lines in that area. Do you know which drain line drains what? Are you certain that water is emitting from the TPR valve? How hot is your water? This could be a dangerous situation. Get a plumber who knows and will explain all your concerns.

i don't know if there is a pressure regulator installed. One of the drain lines is for the drain pan (which is empty), the other is from the T&P valve.
The T&P drain is the one that's leaking. I don't have a temp of the water, i just know that it's not hot enough to peel my skin off. (i'm not home right now, or else i would check the temp).

I just spoke with the plumber who installed the water heater Monday and asked if we can install an expansion tank to see if that fixes the problem. He said that expansion tanks usually go on top of the water heater, and there is no room on mine. It's very close to the roof in the attic.

I am not a licensed plumber, but have been dabbling in it for years. What I do know is that water heaters can be disastrous if not installed properly. A TPR valve that is leaking can mean many things, one of which is exceedingly high pressure, which can make your house explode, killing everyone inside. On the other hand, if the plumber flipped the valve while installing the water heater, he may have allowed sediment to not allow the TPR to seal correctly. In any case, you need to find out why this happened and not waste much time until you know the answers.