I suspect this is more a marketing gimmick than a useful item. While expansive cooling does happen, it is also quickly warmed by the metal around the orifice and in the LP chamber in the first stage so the air entering the LP hose is going to be warmed considerably before even it leaves the first stage. A good metal second stage will also help rewarm the air, which goes through a second cooling at the second stage....the large air chamber, large metal cans and hose lengths are the reason DH regs are so much better than single hose regs in cold water.
The add is also misleading when It brings up the rebreather. Rebreathers do warm the air both from retained body heat and exothermic heating of the absorbent but this heat exchanger has nothing similar. Farther, they actually warm the air, this at best returns it to ambient temperature.
At $350, it's a bit pricey for 4 feet of coiled plated copper tubing. If you are really curious if this works, get 3-4 feet of copper tubing, bend it in a U, add some couplings, insert it in your second stage hose and go diving....and save yourself $300.
If Atomic really wants to accomplish this, redesigning the first and second stages would be the way to go. A larger LP chamber on the first stage, make the first stage of a metal with higher thermal conductivity, add a good metal second stage and add heat sink fins to both stages.