This issue was my fault as I didn't research the topic beforehand.
I expected the process to be:
1) Confirm change in Character Select (CS).
2) Go to Character Customisation (CC).
3) Log-in with the new appearance.
What actually occurred:
1) Confirm change in CS.
2) Choose Race/Clan.
3) Log-in with default appearance.
I never entered the CC. I later learned that I had to save my appearance beforehand, then load it in.
If done correctly, the process becomes:
1) Create appearance in CC & save it.
2) Confirm change in CS.
3) Load in appearance from Step 1.
4) Log-in with new appearance.
This is non-intuitive to me. After confirming the desire to change, it's natural to be given the ability to do so. Instead, you create the appearance, then confirm your desire.
I should have known this beforehand, and it was my mistake. There may have been a way to access the CC in the steps I secondarily outlined, but I missed it, and I'm a bit upset that I wasted a Fantasia.