When I was replacing the hot water heater and the shut off valve I found this issue. Once I turned on my main water I kept the shut off valve closed to the input so I could ensure there was no leak from the replacement. I noticed during this time that the tank was still filling through the output pipe. I turned on the valve for the input pipe and it allowed water to come through (like it should). I did some trouble shooting to make sure it wasn't crossed in installation. So where is the water coming from on the output side? Why is it also filling the tank? Do I have a bad mixer at a shower or sink that is causing a loop?
This is just a guess, but you're probably only seeing existing hot water in your house's pipes flow back to the water heater, since there's none of the resistance that the full tank of water can provide.
Are all the faucets shut off? If one of them is open, the cold would flow back through the 'hot' pipes to the heater.