Refer Campaigns send email messages when a responder completes the form. For Email channel, you can track the emails sent using the Application Messaging Providers separately.
When configuring Moosend or Contact Pigeon Messaging Providers, you can set custom campaign ids. These ids are the default campaign ids used for all emails sent from e-satisfaction
By clicking on the Campaign settings section, you should be able to see the "Campaign Tracking section:
You can set your campaign id at the above input and set all Refer emails to be recorded in the selected campaign.
e-satisfaction supports extra campaign ids for Moosend and Contact Pigeon. You should be able to get these ids from the Moosend and Contact Pigeon dashboards accordingly.
Sub-accounts
If you have a sub-account in either of the above services, ask your master account for the campaign id.