The thermostat has a little hole (like about he size of a wooden Q-tip) that always allows a little water to get past. It's kind of like this, your sea water pump constantly pumps water to the circulating pump on front of the engine, and it also pumps water to your exhaust manifolds/risers. Once the block is full of water and gets to X temperature, the thermostat opens allowing hot water to exit the engine as fresh cool lake water is pumped into the engine. When the t-stat "feels" the cool water it closes until the water reaches X temp again and opens.
That's the short version, looks like your set up has a splitter or manifold, so sea water might go to that manifold then get dispersed to various places. All water exits the engine via the exhaust manifolds and risers.