Honestly, I looked at this problem over a decade ago. My conclusion was, it is safer to add water already prepared for the tank, to the tank. (See above, dose a bucket)
Main reason being I love my fish, the health of animals in my care comes first, the ease of the process is always second to that.
I have never added fresh (untreated) tap water to an overdosed tank and if I had to for whatever reason, I would certainly ensure absolutely no way in the world, could that water affect my fish or the tanks biological situation. There is only one way to ensure that, dose the tank by volume complete.
Now I'm even against this, and I use a water mix prepared by me. Just because in my area things like heavy rain can affect nitrate in tap water. Which is still within the government guidelines but way out of spec for me.