Name only one IMAP server in the ini file, and identify the other one in the Tbird setup.
Example:
DefaultIMAPserver=imap.server1.com
If your username on that server is johndoe, you would set that up in Tbird as
Server Name: 127.0.0.1
User Name: johndoe
But you also get mail from imap2.server2.com, and your username on that server is puppydog. The Tbird account would look like this:
Server Name: 127.0.0.1
User Name: puppydog#imap2.server2.com