Wow, you've got a situation every boon docker dreams of.
But seriously, there ain't no free lunch. How long did you leave the faucet open? It's quite normal for some water to flow out because the system holds pressure.
The only way I can see that water would continue to flow is if the tank itself was pressurized. That shouldn't be possible because the overflow vent should prevent that.
It is a bit of puzzle but I presume that now that you've drained the water we'll all have to wait until you've installed your new faucet to see if you still have a magic water source.