I think your plumber messed up. At least on some Rheem water heaters the top right plumbing is the cold supply supply, and it appears to me that the recirc pump in your case is connected into that cold water supply.
Even if you were tapped into the hot, that's not how my plumbers do recirculating pumps; the plumber puts a new pipe out of the drain connector low on the heater, with one side to the drain valve and the other to the recirc pump. The pump pulls hot water out through the house, through the hot water plumbing, and brings it back through the recirc piping into the heater at the drain fixture.
Edit: To expand on the comment about the drain plug - even if you were tapped into the hot water pipe out, you still wouldn't really be moving hot water out through the house. You'd be pumping water in a circle that doesn't include the hot water in the heater.
Edit again: Taco recommends plumbing recirculators as I mention above.
And edit again: I'm suspicious of the closely soldered copper coming out of the bottom of that pump. Maybe Taco pumps are different, but I'm accustomed to seeing a big flanged dielectric union or other such thing on recirculators. I don't like the 80 degree angle, either. I'd be wondering how long it will be before the vibration and galvanic action and lack of support cause that thing to flop off of there and fill your customer's basement with water.
I just don't like the look of it.