I'm not really sure this is a bug per se. Apologies in advance if this would have done better in bugs. Also, I don't play a transmuter and have no intent to do so probably ever, so I have no personal interest at all in any discussion this might or might not cause. Another player mentioned it, and I agree that something seems objectively off.
Blazebane, charged beacon, and winter mist all seem to be tagged as abjuration spells. They show up in white in spellbook, and a transmuter who once could cast them no longer has the ability to do so.
Helpfiles, both the specific spells' helpfiles and the one listing transmutation spells, indicate that these three should be transmutation. I can't find these spells in SRD or any other supplements online, but their nature doesn't seem to fit at all in the general theme of abjuration, while they do seem at home with the supportive aspects of transmutation. As well, transmutation itself is the school that deals with mutations of the physical makeup of people and things, and that is what these spells presumably do ICly speaking.
Thus I would suggest they be made transmutation spells again, if possible. I gave a look through Areia's spellbook, and these three are the only such mislabeled spells I noticed.
Thanks for reading!
[spells] Mislabled Spell Schools
[spells] Mislabled Spell Schools
Nascentes morimur, finisque ab origine pendet.