It's a native function, but what I'm saying is you need to call it at the right time and right place (like automation). And not just calling it upon the functions.php.
Then please forget about the
_cs_generated_styles and just call
cornerstone_cleanup_generated_styles(). I'm not sure how your tables are named or what post you're looking. But that function should clear them all. What I provided is just an idea as I initially thought that you have a way of automating the process
It should work on multisite, the function
cornerstone_cleanup_generated_styles() is just a shortcut for this
$wpdb->delete( $wpdb->postmeta, array( 'meta_key' => '_cs_generated_styles' ) );
global $wpdb; hold the current database of the current site (that belongs to multi-site, or the single-site itself).
And you don't have to create a MySQL query, but again, what was provided are just idea as I'm not sure of how you'll automate it (my initial thought is Cron Job).