You can set the default notifications sent from SocialEngine PHP to the member’s in-site inbox by following this guide. This can help control which notifications new users see in their mailbox when they log into the site. Note that this only controls the notifications on initial sign up. Individual members can change these settings in their Notification privacy section.
Navigate to Settings > Default Notification Alerts.
Check to enable or uncheck to disable the in-site notifications and Save Changes when done.
Remember to clear your cache!
This will only work for new members and will not affect current members.