Hi Dom!
Thanks for getting in touch with us!
Unfortunately, that is not a built-in functionality of our plugins. By default, event organizers is a custom post type that is linked to the events.
If you want users to only have access to their events, you should take a look at our Community Events plugin.
Additionally, let me share with you the following article that might be of help which gives an overview of how you can create a members only calendar > https://theeventscalendar.com/knowledgebase/making-members-calendar/
I hope that helps. Let me know if any follow up questions.
Best,
Victor