It is T'ed into the cold supply.FWIW, in the city where I live, to pass any plumbing inspection with a WH, an expansion tank is required. Check your local codes. They also require a tempering valve to be installed. Depending on where the tank is, a vacuum relief valve might also be required.
So, if I follow your description, the return line comes out of the wall, goes to the pump, then is T'ed into the hot supply? Maybe I'm missing something, but wouldn't that just be pushing the cooler return water into the hot outlet? How would that line get warm? Without a check valve (might be one in the pump), when you open a hot valve somewhere, you'd be pulling water from both the hot line and the cool return line.
You want to be pushing, or pulling the hot through the hot line, then returning it to the cold side, often the lower drain line of the WH is used for that, but it always requires a check valve to prevent pulling water from the return and hot line at the same time.
We do get hot water everywhere we should; it just takes a while if hot water hasn't been run for a while. My current thinking is to have the plumber drive it into the drain line which is what he said he's done for all his WH installations.