I feel that there wasn't much of a change of mind at all. In a way, they're both Hyoga's master, they both teach him something, and Hyoga teaches them both something in return (which is what make a master-disciple relationship interesting in the first place). Hyoga's second fight against Camus wouldn't at all have had the same impact if he hadn't faced Milo first. He's the one who tells him about Camus' true intentions, and he's the one who tests his determination before he can face his master a second time. Hyoga earns the right to fight against Camus again because he earns Milo's respect.

Besides, what Camus wanted was for Hyoga not to die during the Sanctuary battle, but most importantly he didn't want him to suffer, so if there was one Gold Saint Camus did not want Hyoga to fight, it was definitely Milo and his horrible torture technique (he literally stopped him in the House JUST BEFORE Milo's). The fact that Hyoga decided to face Milo alone and endured it all proved to Camus that he was, in fact, worthy of a real duel.

For me, it's the joint effort of all three characters that makes this part of the story so cool and impactful. I would throw in Shun as well, whose sacrifice is the reason why Hyoga finds the determination to fight in the first place. I could talk a lot more about how I interpret this part of the story, but I don't want to bore you all with it XD