Is water coming out the refill tube? Is the refill tube directed into the overflow tube. You should not need to replace the supply tube from the shut off valve to the refill valve. In regards to the leak. If it is leaking at the retaining nut then do you have the valve and washer centered in the opening? Did you clean any debri off the porcelain? Do you have it tight enough. This connection needs to be tight. If the leak is where the supply tube meets the valve then you may need to replace the washer or if it is a white hose the washer may be indented and you will need to replace it. There is a good explanation of how toilets work in this forums reference library.