"After you finish rearranging your "Playlist", please pause the episode that's currently playing and resume by tapping it in your "Playlist". This way, the episodes in your "Next up" list will be updated to the same as those in the Playlist that you have just arranged.
You can also rearrange the order of the episodes in the "Next up" section and all changes made there will be applied instantly."
More here: https://castbox.fm/help.html?qatag=Playlist
If you are still encountering problems, there's possibility of it being a bug.
Hi! Thanks for your message. Have you tried to upload audio files via our web portal? You could upload episodes via this link - https://castbox.fm/creator/upload. Please make sure you log in your account on the website first. : ) Hope this helps! - Sophie
Hi! Thanks for your message. Do you mean you were trying to access Playlist via Castbox website? Could you please click this link - https://castbox.fm/my/playlist to see if it could work well? Please make sure you log in on the website first. Hope this helps! - Sophie