Your definition for "supernatural" is correct. But you are assuming that if there was a "creator", then he/she/it was supernatural.
Whatever your preferred definition of "God" is, if there were evidence for Him, then it would bring that God into the natural world.
That some faithful people claim that God desires to remain unmeasured, and unseen, in the realm of the supernatural is merely evidence in my eyes that they know God does not exist and do not wish to face that fact. I believe they live in a fantasy world, and they like it that way.
It takes a lot of guts to admit that when one dies, that's it, the lights go out. I wish I could lie to myself and believe that I would spend eternity in heaven. It would make life a bunch nicer. But I find it impossible to lie to myself.
I believe that God is supernatural in the sense that He is and can operate outside the physical, material universe. But I also believe that He can manifest Himself in the physical world. Either physically by direct intervention or by displays of His power. I think that what we call miracles is evidence of that. Now the problem with that is that while many miracles are documented, catching one while it's happening to record it and analyze it is a different matter. I don't know of any that have been caught in the act.