To unlock color variations, that has to be done on the character with the Artifact and in the case of the Mage Tower the character who completed that questline and fight.
So to answer your question here, it’s the 110 original character who you need to use to unlock the other colors, the one who actually finished the Mage Tower fight.
Once you do that and earn these other colors, then those become part of your Transmog collection and other characters of the same class will be able to use those (spec limits apply) afterwards.