In order to have TLS work with SquirrelMail you need to start the configuration script at /usr/share/squirrelmail/config/conf.pl   When the script opens choose “Server Settings” and then edit the IMAP port settings and change them from port 143 to port 993.

SquirrelMail Configuration : Read: config.php (1.4.0)
———————————————————
Server Settings

General
——-
1.  Domain                 : localhost
2.  Invert Time            : false
3.  Sendmail or SMTP       : SMTP

IMAP Settings
————–
4.  IMAP Server            : localhost
5.  IMAP Port              : 993
6.  Authentication type    : login
7.  Secure IMAP (TLS)      : false
8.  Server software        : uw
9.  Delimiter              : /

B.  Update SMTP Settings   : localhost:25
H.  Hide IMAP Server Settings

R   Return to Main Menu
C   Turn color off
S   Save data
Q   Quit

Restart Dovecot and httpd and you should be able to login to SquirrellMail using the https on the browser and the encrypted communication on port 993 for Dovecot.  To the user the only decision they need to make is to accept the self-signed certificate and point their browser to https.