How can I ensure other persons receive notification when someone submits a response?

You can check the email history logs to see if the email recipients is receiving notification emails or in the bounce list. Here's a guide: https://www.jotform.com/help/293-How-to-View-All-Your-Form-Email-History. 

Also, The Test Email button in the notification email settings will only send to the registered email address of the account. You need to fill up the form manually and click the test if all email recipients is receiving the notification emails. 

Hope that helps. If you have questions, please let us know.

Related guides:
Why-I-am-not-Receiving-Email-Notifications
Send-Notifications-to-Multiple-Recipients