So I looked through every question on the rules forum and read the book three times and see no mention of this.
Once you level up and choose a "branch" does your tier III card have to be in that branch as well. For example, if I'm playing Dodger and I have chosen Finger of Death as my tier II red and I have leveled all my slots to tier II, can I choose Blazing Skull or am I "locked" into choosing Middle Finger of Death?
Nope. You are free to jump between them.