As well as the cron jobs, this also depends on where you are displaying the text and were you are getting it.
I recently did a similar thing for some events (not Wix Events.)
The text/image urls etc are retrieved from a CMS and the dataset is linked to repeaters.
it will show for the day it’s scheduled for taken from a CMS date. It will then be removed from the CMS when it becomes stale. There is background code to do all of this run by the cron jobs. But to make sure in my case the repeaters update if someone already has the page loaded, there is code to publish the changes.
My code also has a collapse expand behaviour if there is no event for Today. Which save unless any blank space on the page.
I will share how this was all done when I get a mo.