If you connect to Jellyfin through Kodi with the JellyCon add-on, you can sync audio, subtitles etc. when it's playing.
While it's possible to navigate through your Jellyfin libraries from within the Jellycon add-on in Kodi, I usually find it quicker to just use the Jellyfin app or webapp on phone/pc to find the desired media, then "cast" it to the active Kodi client. The Kodi client will then play it directly from the server, no video data is going through the casting device.