Basically, unlike with a lightning bolt, which is just made and sometimes aimed with the weave, a fire ball is actually maintained with the weave, so that once the weave is gone, the fire has nothing to fuel it, and just dissipates.

Which isn't to say the one wearing the medallion isn't going to get singed a little, just not the "turned into a pile of ash" that normally happens.

As for why they don't get more singed then they do...

The only thing I can think of, is the weave actually extends a bit outside the fire ball itself(like the weave forms a ball that ignites a fire the in the center of it), and so touches them before the actual fire does.