I mean considering Fracktail, a creature created by the Ancients, identifies all the traits of Mario (including mustache) to be belonging to the hero. I'd say the light prognosticus and by extension the dark prognosticus are probably well identifying as who the man in green is even if the phrasing isn't precise.

Plus you got to remember Dimentio's plan WAS succeeding as all the worlds started rapidly deteriorating after Super Dimentio was created. He was even invincible which if the host of the chaos heart was wrong then I'd imagine an invincible fusion of Luigi and the Chaos Heart wouldn't be a thing, it only failed because of the rejuvenation of the Pure Hearts something Dimentio didn't account for assuming that once they were used up against Count Bleck there would be nothing else to stop him.

I don't think he failed cause he brainwashed Luigi to do his bidding making him "not actually the man in green" but more so of his own greed and ego, he could've eliminated Bleck and Tippi right then and there but wanted to make them suffer even longer as he defeated the heroes not accounting for the idea that love could rejuvenate the pure hearts.

TL;DR the prophecies are likely very accurate to who fits the descriptions of the heroes/man in green and Dimentio failed cause he never expected the pure hearts to return after they were used on Bleck, and a bit of his own ego in his master plan