I think the problem is that whilst you've changed the Facebook account on the device, the app needs to be 'hard closed' and restarted before it'll recognise the secondary account.
I'll give you a step by step tutorial.
Firstly, fully close the Top Eleven app by double tapping your 'home button' and swipe up, like so.
Then go to settings - Facebook, and click your account name, then 'delete account' like so.
Put in the secondary account details once deleted, and log in.
Then it's just a case of opening the Top Eleven app again and it'll automatically log in with the second account.
Rinse and repeat to get the old account back.