Water use in nuclear reactors is primarily by the generator. What you describe is a once-through system where the water used to generate steam is dumped into the source along with the condensed steam. Many nuclear plants no longer use this system due to the massive amount of water required.
There are a few ways to decrease water use, but most likely the TSMR is using a dry cooling system. It would essentially act like a car's radiator and the steam is essentially air cooled, probably assisted by a fan, and then recycled back into the generator. It would reduce efficiency, but not as much as with current plants due to the higher temperature of the primary cooling circuit.