I found that if I followed the demonstration video exactly as shown ( Link ) the Barracks options do work.
In my case, I navigated to Barracks --> VIEW SOLDIERS --> select a soldier from the list --> select ABILITIES --> press the desired Barracks option --> press the desired increment/decrement value option --> select the "next soldier" arrow button and then return back to the original edited soldier. The changed value(s) should now appear.
If you haven't already done so, please try starting over from the beginning (i.e. delete the trainer, clear the cache from your browser, then re-download the trainer). The 126.96.36.19965 trainer itself was first released on 11/8 and less than a day later an updated barracks fix was posted, so perhaps you had somehow acquired the original unfixed version?
Follow through the troubleshooting guide if needed ( Link ). If you are still having problems with the trainer, please list out what you HAVE done (along with your system specs; are you running Win 8? Are none of the other trainer options working?) and maybe someone else who had a similar situation can relate and offer another solution.