That is a rather confusing word picture....
The shiny tank at the front of this engine is not an "over flow" tank, it is a "surge tank" (OK, expansion tank then). No water should leave this tank, period, under any circumstances at any port, when the engine is cold. When the engine is HOT and the water has expanded enough to totally fill this surge tank beyond it's capacity AND pressure rating of it's "radiator" cap, THEN it will expell a certain volume of water to the "over flow tank". Assuming you have an overflow tank, not all cars do. If you don't, the water is simply lost to the atmosphere (hit's the fan and is blown all over the engine) and will not be returned by "suction" when the engine cools back down.
IF water is leaving the SURGE TANK (see the shiny tank in the picture) when the engine is cold, the reason is elementary, my dear Watson: The radiator cap isn't holding pressure.
