@Marieke
The reminders from DocuSign are related to an envelope, where an action is pending. After you voided the envelope, there will be no additional reminders for that envelope. In case the recipient still receives reminders, there must be an additional envelope waiting for them, which has reminders enabled.
The person should click on the DocuSign link in the reminder email to get to the actual document. If they do not want to sign it, they can choose the “Decline to Sign” action in the top navigation to void the envelope,. This will stop all future reminders for this envelope and the sender will be notified as well.