What you're seeing is correct. Wet exhaust marine engine cooling systems are quite different to automotive cooling systems. The marine engine needs water continuously flowing through the exhaust system to keep the manifold, shutters and everything downstream cool. The water in the engine just circulates until it's warm enough to open the thermostat, then that water is 'dumped' and cool water replaces it until the thermostat opens again. When the thermostat is closed, the water being drawn up by the impeller in the drive 'bypasses' the engine and is dumped straight to the exhaust manifold (cooling jacket), then out through the drive/exhaust reliefs.... The exhaust cooling water and the exhaust gases are mixed (so the gases are cooled) at the outlet of the elbow, just above the shutter...
Hope this helps,
Chris........
