If you want everything to be user@students.kcai.edu, set
$domain = 'students.kcai.edu';
or maybe
$domain = implode('', file('/etc/hostname'));
The real question is, how does squirelmail know that it's on the "squirrelmail" host? When you find that out, you've solved the problem.
Most of the time, I find that Squirrelmail tends to pull the hostname from the Doamin name as entered in the web browser. I think it's a config issue in the files, but I am honestly not sure. there's a way around it.