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 take 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 usually display quickly — often within a few hours".
It's not unprecedented for podcast apps to take up to 24 hours to refresh feeds and display new episodes. Apple Podcasts allows podcasters to manually refresh their feed, from within Podcasts Connect.