That's definitely what it is, it's clearly tied to emotions and theana he sees all the time so the "rainbow" is probably just some story about a powerful mage who was powerful because he was a really emotional guy and the story was just twisted over a long time
LMAOO you're totally right, there's no way author keep showing us the rainbow mana that keep floating around Ray without meaning. He also can actually choose which color he wanted to get the ring (?) that's totally what rainbow means here I suppose
I think the rainbow is someone like an arch mate with 7 circles of mana each a color. Completing the spectrum.
would be extremely funny if the "rainbow" they're looking for is the mana within the air that ray sees everyday lol