Short answer: When a result is ready, authorized contacts receive an email telling them to sign in to the portal. The email does not contain the result itself.
When new results are published to your portal, each active contact who has the Test Results permission receives an email asking them to sign in. For privacy, the email contains no test details. If a report is corrected, you receive an "Updated results" email. There is no separate on/off setting: to stop these emails for a contact, email support@odoseklabsolutions.com and our team removes that contact's Test Results permission. This also removes their access to results.