The owner can be set via the data export configuration page, that you can access either via the persona settings page or your account settings page. Simply look for the configuration button and click it.
This will open the app configuration modal, from where you can set the owner or email associated with the exported contact. See below for how to set the email inbox for the Outreach app.
Keep in mind that the oauth user needs to have admin access to the app, in order to allow you to configure the whole data export.