The webmail program (Uebimiau) is it's own self contained program. Since it uses pop to view messages, it has to download them and store them to it's own temp location. This location is totally independant of any system qutoas setup by DirectAdmin.
To change the email quotas imposed by the webmail program, you must edit
/var/www/html/webmail/inc/config.php
and change the $quota_limit value to whatever you want:
$quota_limit = 20480; this is 20 meg. Using other programs such as squirrelmail which use imap will not run into this issue.