That means it is not triggered correctly. About your configuration on cronjob? On diagnostic panel, enable the logs at debug level, then on wp-content/logs/newsletter/main-xxxxxxx.txt there is a file which should report if the cron is called every five minutes.
Ask them to setup a 5 minutes cron that calls your wp-cron.php. More indication on my page dedicated to delivery engine, start from https://www.thenewsletterplugin.com/plugins/newsletter. A technician must be able to setup this kind of simple system administrative procedures.