What I want to know is when did people start considering it to be factual account of something that really happened.
Certainly by the time of Josephus (Antiquitates Judiacae, 9.208-214), who reported Jonah's adventure with the fish and preaching in Ninevah as historical events. There is a good article on this by Louis Feldman ("Josephus' Portrait of Jonah," in Studies in Josephus' Rewritten Bible, 1998) who shows that Josephus toned down the satirical aspects of the story -- omitting such things as Ninevah's wholesale repentance, animals wearing sackcloth, and the incident with the gourd plant. Josephus handles the difficulty of the inappropriate prayer by having Jonah deliver it after he was vomited out (whereas the LXX and later exegetes reworded the prayer to make it more appropriate). Similarly, he eliminates the comic image of Jonah sleeping and "snoring" (as per the LXX) during the tempest by having Jonah go down into the hold and lie down (not necessarily to go to sleep) in order to abstain from the idolatrous praying done by the pagan sailors (Antiquitates, 9.209). But Josephus is stuck with the fish story that is such an integral part of the Jonah narrative, and so he reports it matter-of-factly but qualifies it by saying that what he relates is how "the story has it" (Antiquitates, 9.213). The fish story however was widely used by pagans to sarcastically ridicule the beliefs of Christians (cf. Origen, Adversus Celsum 7.53; Augustine, Epistulae 7.53).
Earlier allusions to the story do not clearly take it as literal. The author of Judith (second century BC) reuses the story of Ninevah's repentance in 4:9-15 (including the motif of animals wearing sackcloth), but since this was a work of fiction it is hardly evidence that the author thought Jonah to be historical. Similarly, a reviser of Tobit 4:3 replaced the reference to "Nahum" with "Jonah", but again this is within a piece of historical fiction. The gospels use the story of Jonah allegorically in Matthew 12:10, Luke 11:30-32, as typifying the "sign of Jonah" in Jesus. The reference to the coming resurrection of the men of Ninevah who "repented at the preaching of Jonah" (Luke 11:32) could be taken as presuming the historicity of the story, or it can be taken as an illustration without necessarily requiring a strictly historical basis of the Jonah story. It is worth recalling that outside conscious historiography, there was no sharp distinction between legend and history as we might have today. Paul for instance refered to the midrashic legend of the rock that followed the Israelites throughout the wilderness (1 Corinthians 10:4), and he used it as a didactic illustration, but this does not necessarily mean that he thought of the travelling rock as strictly historical. It is also worth noting that later Jewish midrash amplified the satirical content of the story even further and increased the number of fantastic elements of the story, cf. Pirqei de Rabbi Eliezer 10, which Yvonne Sherwood characterizes as a sort of Jewish Twenty Thousand Leagues Under the Sea. My favorite comic moment is the one in wihch the sailors try to throw Jonah into the sea but they are stuck in a catch-22 dilemma of either killing themselves by keeping Jonah on board or killing a possibly innocent man by throwing him overboard, so they partially dunk him in the water (first to his knees, then to his navel, then to his neck, and then entirely) and take him out again in order to see if Jonah's god would be satisfied without throwing him entirely overboard, with the effect of making the sea agitated and then calming it and then making it agitated again, and then calming it again, over and over. The fish then gives Jonah an extensive tour of the underwater underworld, each location occasioned by a line of his psalm that he sings as he visits this realm. Another midrash (Midrash Jonah) has it that Jonah was so comfortable inside the fish that he didn't give his psalm even after three days, so God made a female fish swim alongside the male fish that had swallowed Jonah and she demanded it to spit out the prophet or she would swallow the other fish whole. The male fish then vomits out Jonah and the female fish swallows him, where Jonah discovers to his horror that this fish was pregnant with 365,000 baby fishes and being cramped with the slime and tons of baby fishes all over him, Jonah finally yielded up the prayer that God required. It is hard not to see this as the kind of satirical humor it is.
One interesting theory is that Jonah originally was an excerpt from either the lost Midrash of the Book of Kings mentioned in 2 Chronicles 24:27 or the lost Words of the Seers mentioned in 2 Chronicles 33:19. This fits well with the fourth-century BC date of the Chronicler. This is especially tempting since the Chronicler mentions individual works like the Acts of Samuel the Seer, the Acts of Nathan the Prophet, the Acts of Gad the Seer, the Visions of Iddo the Seer, the Midrash of Prophet Iddo, etc. The original title of Jonah could well have been the Acts of Jonah the Prophet or the Midrash of Jonah the Prophet. The latter would have been rather appropriate for the kind of story found in Jonah, which (while not belonging to the later genre of midrashim) is haggadaic and evidences midrashic activity in weaving OT content to develop a new didactic story. If it was excerpted, one reason may have been to fill out the colection of Minor Prophets to the desired number of twelve. It is kind of the odd one out -- being mostly narrative and containing very litle of actual prophecy.
