After you've added an episode to your feed, it's only natural that you'd want to see it published on Apple Podcasts and other podcast apps ASAP. While Omny writes any changes you make to your RSS feed immediately, Apple Podcasts, Spotify, and other major podcast apps will need more time to reflect new episodes or other updates to your feed.
This is because these services check your RSS feed on a scheduled basis from their servers, and then display changes or new episodes for your listeners when they see there's been an update.
Each of these services operate different refresh schedules. For example, Apple Podcasts states "changes will be displayed within 24 hours".
In reality, it should take much less time than 24 hours to see your changes reflected on Apple Podcasts and other podcast apps but it all depends on their ‘check-in’ system. There is no ability to manually perform a refresh or configure services to refresh your feed any faster than it otherwise would.
Unfortunately, this part is out of our hands but if you do notice that your episode is taking longer than usual, please feel free to reach out to your support team to let them know.