So, the hero Rayman was originally a bog-standard warrior hero just like Albus. He may or may not have managed (it isn't clear from the flashbacks) to complete his bog-standard quest with a standard hero's party just like Albus, but at the cost of his beloved Risa. So he Revolved to try to save Risa but, unlike Albus who sped up his recruitment drive and strategically placed multiple members of his party in places where they could multiply their contributions (up to and including leading large armies), Rayman came to the wrong conclusion and decided to go solo. He then took the somewhat selfish step of abandoning the original heroic quest to become a healer in order to save Risa. It's also possible (from the flashbacks) that originally in Rayman's timeline the Red Blight was far worse than the demon war itself, which means his decision might not have been that selfish after all.
On his 29th quest Rayman partially finished the cure for the Red Blight, left it with Risa, and probably got defeated in combat against monsters (because he was running solo and had specced himself as a healer instead of the original OP warrior he had been) while searching for the components that Albus' party managed to get in this adventure. So he was forced to Revolve, except this time it didn't start a new loop because Rayman instead got unstuck from spacetime. So Rayman's 29th loop continued with Risa finishing the cure and ending the Red Blight. This started Albus' first loop, in which the Red Blight took the life of his caretaker but wasn't that big of a deal elsewhere thanks to Risa's cure. Because Albus always Revolved back to a point in time after Rayman's disappearance, to him the Red Blight was always already solved and thus just a personal tragedy but not the world-level threat it was to Rayman. Nobody even knew of the Hero Rayman because he never went to see the king or formed his party, having abandoned the hero's quest in favor of curing the Red Blight. Nobody even appreciated his contribution because in Albus' timeline the Red Blight wasn't all that bad. However, SOMEONE still had to fix the Demon King issue, so Albus became the hero instead and finished the quest in place of Rayman at the cost of his own life.
Fiona and the gang then proceeded to massively screw up and Revolved everyone into Rayman's "30th loop", which originally never happened, causing the Red Blight to get out of control, or at least as bad as in Rayman's first loop. So Albus had to fix that problem by distributing the cure.
In this sense, the statement that Rayman was the hero "this time" actually means that Rayman HAD ALWAYS BEEN the intended hero, not Albus, and the turbo-Revolve sent them to the timeline where Rayman had been the hero before Albus was chosen as his substitute.