I don't have i, I use android but let me tell you how it works.
Might help.
First, I have the app as an individual button in my screen .
This goes to topeleven.com version and not to fb app.


In the mobile I go to settings > log out > log in with fb >type the mail of the fb and paswd of account B I have > connect

In the tablet, I go to fb app, I must disconnect A and connect to my other account B, then I go to the game (from the button in the screen), then I go to settings and click the log in with fb. (then it reads the new fb and starts with the B team).
If I want to go back to A team, then I go again in fb app, disconnect B, connect with A, then back to the game again and log in.