The customer support ticket submit form is displayed to all users and visitors of your site. If a visitor submits the form, the ticket's author is recorded as visitor. Visitors get an email notification after they submitted a ticket. They can search with their ticket id or email to access their own tickets. They can also go to their ticket pages. Visitors submitted tickets are publicly accessible.
If a registered WordPress user submits a ticket then the ticket author is saved as that user. This ticket will be displayed only to the user who submitted the ticket.