Website needs to be opened for wp_mail to work

This plugin uses WordPress CRON API. Its no the same thing as usual CRON jobs available at cPanel dashboard. The difference is in the way how they are executed.

When somebody visits your site, WordPress checks if there is a scheduled job which has to be run, then WordPress runs this job by initiating a separate request to a specific URL. If nobody visits your site, then your CRON jobs won’t be run even if they are already overdue…

In other words to run WordPress CRON jobs in time you have to have visitors on your site. Another option would be to ping your site by using special service…