When you create custom fields for your Joomla! users using ARRA User Migrate, they can’t be set as required by default. There is needed a hack in core Joomla! files, so if you do this is your choice. You must replace profile-joomla3.x (unzip downloaded) over the one from your server (path to file is plugins/user/profile/profile.php) – make a backup of original one just in case.