This is similar to the uploading CSV file and autogenerate password.
What database field is set that causes the cron.php to process that user and the password reset?
You mention a campus management system, so I wonder if you're perhaps going about this backwards. Moodle can authenticate from external sources such as LDAP/Active Directory, external Databases, SSO etc - so if you authenticate from that source, rather than rely on internal accounts and passwords in Moodle (they will still have a record in mdl_user table), it will mean a smoother integration with your other systems rather than potentially different passwords for different applications - a support nightmare.
But, to answer your actual question, password resets aren't handled by Cron specifically. You set a user preference called 'auth_forcepasswordchange' with the value of true.
set_user_preference('auth_forcepasswordchange', true, $user->id);
On next login, the user will be forced to change their password.