First of all, I had the exact same problem with my flash animation, and I learned how to fix it, it has nothing to do with ADPCM (well it depends, for me ADPCM didn't work at all)
It might be a good idea to do that ADPCM stuff since it doesn't seem to do anything bad things, but if that still doesn't work (such as in my case) then there is another easy solution.
On your timeline, click on the first keyframe where your sound starts to play. Then on that box in the bottom, you should see something where it says Sync:
Just click on the first drop down box and change it to "Stream". The sound should sync perfectly after this. If it plays perfectly in your project it will play perfectly when you test it.