Stepping back on your question, what do you mean that the water was running out of the bowl? Inside the tank, you will see the fill-valve. This is where the replacment water enters the tank. You should also see a plastic tube sticking up near the center of the tank. This is the overflow tube. If the fill-valve is not set correctly (to shut off) , water will continue to run after flushing and exit through this tube. This would need an adjustment on the fill valve. At the bottom of the tube is a large rubber piece called the flapper. If you push the flush handle, you will see the flapper raise up, allowing the tank water to flow to the bowl. Sometimes they go bad and need replaced (simple job) or you can clean the sealing surfaces with a rag. Sometimes, deposits collect there and prevent the flapper from sealing completely. Also make sure the chain/strap that raises the flapper is not hanging up and preventing the flapper from dropping down and sealing. As far as disconnecting the supply tubing at the supply valve, this is why I said to hold a rag over the valve when turning on. You only need a quick on/off to know if water is flowing through the valve.
