I am using WP Job Manager. When a new job is being submitted via front-end form, the regarding PSN rule does not create notification emails. What could it be?

We know of that issue on WP Engine hosted servers. Their object cache prevents the events on front-end post submission to be executed. Please deactivate WP Engine’s object cache on your dashboard and purge all caches. Read more about the WP Engine cache on WP Engine support