I think J. Vernon McGee was known for teaching this on the radio for many years. Not that he was the first to teach it but he did make it popular with his radio platform and charming personality and being a generally solid fundamentalist preacher, he caused many to accept it as true.
I never understood it that way from the first reading and was shocked when I heard McGee teach it. I thought McGee was smarter than that. The sign of Jonas was just that "A sign" A shadow, a Type, not the real.
Then Jonah prayed unto the LORD his God out of the fish's belly,
2And said, I cried by reason of mine affliction unto the LORD, and he heard me; out of the belly of hell cried I, and thou heardest my voice. (here he is in the belly of the fish when he says out of the belly of hell I cried. CONTEXTUAL CONTEXT requires such an interpretation. He is calling his condition the belly of hell as it would be such a miserable place and he is using poetic license)
3For thou hadst cast me into the deep, in the midst of the seas; and the floods compassed me about: all thy billows and thy waves passed over me.
4Then I said, I am cast out of thy sight; yet I will look again toward thy holy temple.
5The waters compassed me about, even to the soul: the depth closed me round about, the weeds were wrapped about my head. (Is there sea weed in spiritual hell?)
6I went down to the bottoms of the mountains; the earth with her bars was about me for ever: yet hast thou brought up my life from corruption, O LORD my God.
7When my soul fainted within me I remembered the LORD: and my prayer came in unto thee, into thine holy temple.
8They that observe lying vanities forsake their own mercy.
This is not even the least bit confusing. He was clearly talking about the fact that the fish took him down to the bottom of the ocean and somehow Jonah probably could feel the pressure and knew he was at an awful depth and he had SEA WEED WRAPPED ABOUT HIS HEAD... that part was probably recorded because God knew someone would think Jonah had died and gone to hell and been resurrected if that detail was not included. That Jesus pointed to it as a TYPE or sign means that it was not that Jonah literally did what Jesus did. Theologically Jonah could not have been the first. However it does give us another reason to believe that Jesus did descend into the lower parts of the earth after his death as this is still debated.