I'm pretty new to this software and I have yet to buy any version, my plan is to test the software extensively and get to know it first as the price tag for Pro is a little high. However I was using the same method that you mentioned here, I just cannot export yet for the simple fact that I am using the trial still, so I haven't noticed the problem that you've run into here, although I did notice something after some time playing with the software which might be the solution for you...
There is a feature for 'Flipping' joints already... Here is an image of the over all interface so you know where I am at: http://i.imgur.com/LG8Zwjr.png Then look to the bottom right, once checked you can see the result here: http://i.imgur.com/mFWdCeN.png
I hope this helps you a little at least... I am still learning things myself, hopefully this works ok when exporting to Unity.
Kind Regards,
Patrick.