The cache often creates confusion when new events do not appear immediately or disappear instantly when deleted.
By default the cache period is 24 hours so new events will not show up for up to 24 hours.
This helps the performance of your site and reduces the calls out to Eventbrite.
In the premium plugin you can change the cache time and also force a clear. Go to the settings page, Manage Eventbrite Cache tab, set the cache to a short period and tick the clear cache tick box. They should appear.
Once you have finished testing or changing events, reset the cache to a longer period ( e.g. 1 Day ) to protect your website performance.