Most of the V6 and V8 engines with raw water cooling use a supply pump and the normal engine manufacturer's circulation pump. The supply pump is normally eeither in the outdrive, belt driven beside the front of the engine, or mounted on the front of the engines crankshaft. Sometimes it takes a little time for the water to get through the outdrive, through the supply pump, to the engine to fill it up, and start to come out the outdrive. This can be 20 - 30 seconds or more after engine start. in addition to seeing the water coming out the bottom side of the outdrive, you should hear a difference when the water enters the exhaust system and muffles the exhaust. I had a situation one year where the engine did not fill with water nearly this quickly. I ran the engine twice for about 40 seconds each time without seeing water coming out. After filling the block with water the engine acted normally then, and for many years afterward. Since then I have pulled the large hose at the thermostat (or another connection near the top of the engine) to fill the engine block so it does not lack cooling during start up.
The Muff used should fit snugly and stay in place. When the water is turned on you should have water escaping between the muff and the outdrive. This should continue while running the engine. I never rev the engine above about 1200 to 1500 rpm, except for maybe a brief check to see that the engine accelerates well, and to satisfy my desire to hear it.
You may notice that the engine requires more water than the hose is providing, and water is not escaping from the muff at higher RPM. I also install a small garden hose shut off valve between the hose and the muff to reduce the time and distance between turning the water on and starting the engine. As previousy stated, watch and listen for leaks and anything unusual.