iThemes Security Pro uses the WordPress provided code to trigger the automatic plugin and theme background updates.
When automatic plugin and theme updates are enabled on a DreamHost hosted WordPress website, WordPress Core returns the
WP_Automatic_Updater::is_vcs_checkout which is relayed in the iThemes Security Version Management settings as
Warning: Due to server or site configuration, automatic updates may fail to install automatically if enabled.
The reason for the error is the .git file in the site's directory that DreamHost uses to create new sites, and WordPress Core won’t perform any plugin and theme auto-updates because it detects its a VCS checkout. Unfortunately, this means that DreamHost hosted sites aren't going to be able to use the WordPress background updates for plugin and themes. So due to the DreamHost server configuration, you will not be able to use the Version Management auto-update options in iThemes Security Pro.
It is worth mentioning that basic controls for auto-updating plugins & themes is coming to WordPress 5. So this may change in the future if/when DreamHost adds support for that feature, you will be able to use the iThemes Security Pro Version Management to update your plugin and themes automatically.