OK - I'll give this a stab as I just last night put a Jelly Bean rom on my SIII and was able to get video playback.
This is the ONLY way I know how to do it.
First, you have to see your video files in the app. If you have a folder defined in the Subsonic Media files panel as C:\Videos you have to place the video files in subfolders as the app will not look for files in the defined root. So for wxample if you have files sorted by type you would have files in C:\Videos\mp4files\sample.mp4 and so on. Don't whine - it's just the way it is.
Second, on Jelly Bean you need to install flash which isn't as easy as it sounds as everyone today is conspiring to eliminate flash for everyone even though the promised alternatives aren't available to many of us - go figure - the central committee has spoken.
You can find the instructions needed to install flash on Jelly Bean here:
http://liliputing.com/2012/07/how-to-in ... vices.htmlOnce you have flash properly installed the app will call the browser you select and start playback. I setup the default browser for Subsonic as I couldn't figure out how to prevent Dolphin from updating and the latest Dolphin block flash.
That's how it's done on Android JB. I dropped back to ICS because Wifi Tether isn't running on rooted JB yet, but I had it running fine on JB last night.