I have never seen Tiana in Tokyo. To be fair, though, I haven't seen Rapunzel, either. And I almost always go to DisneySEA rather than Tokyo Disneyland.
Where merchandising is concerned, however, Tiana was like a phantom. On the contrary, Rapunzel has/had a HUGE presence in the Disney Stores and all over Japan. Not so much the parks, though, at least not DisneySEA.
Mulan is not a princess. Neither is Alice, nor Wendy. Tiger Lily is, though. And so is Kida, who is my favorite because she is actually a leader who makes choices and guides her people. It's not just a token trope title for her.^^
Mulan IS one of the "official" Disney princesses, I believe. The "official" list is: Snow White, Cinderella, Aurora, Ariel, Belle, Tiana, Rapunzel, Mulan, Pocahontas, and (if the current Disney merchandise booth at the NYC toy show is to be believed) Merida.