So, what exactly is the story?

[Blackdrazon]

It could, however, be excused by the simple fact that after the war we're just playing, everything was completely annihilated. The worlds we visited in that storybook were recreated as individual worlds from the hearts of the kids who remembered them - so naturally, eventually the same characters from back then would revive, as well.
We don't know if a freshly (re)created world needs to start in dinosaur age or can just pop into existance with all it's backsory in tow (I'd be guessing the latter is at least possible), but I guess this might explain the time gap between those worlds in Chi and the main plot line.

It was also mentioned that back then, there was only ONE world in all (I'm guessing that would be Daybreak Town), so maybe the other worlds are just stories in a picture book that became real when the Multiverse was created.

Yes, I was wondering about this. They may also have been sleeping somehow, in the world of dreams from DDD perhaps, and only woke up a short time before KH1. Maybe Maleficent - who has power over sleep, I'm realizing as I type this! - drew them out of dreams to fetch back the princesses? It would explain Dwarf Woodlands, Agrabah and Wonderland, though not Olympus Coliseum. (I think it is intentional that we're seeing Princess' worlds in this game but I don't necessarily think it's because my theory is correct.)