You'd better turn off TLS/SSL in TB and let Avast handle it.
http://napoveda.seznam.cz/cz/imap-pop3-smtp.html
Let Avast handle what, exactly? Does Avast 2014 provide server authentication and/or encryption like SSL/TLS? There's nothing in the documentation that says that it does, so I'm not clear.
The program does clearly say, however, that it can now scan your email, even in a mail client with SSL/TLS enabled. To me, this means we shouldn't have to disable SSL/TLS in TB. But either Avast and TB no longer play nicely, or nobody has stumbled upon the correct configuration.