I sent an email to alienbees regarding to this issue. Here is the answer.
The Umbrella Adaptor fits inside the center chamber of the ringflash in place of the front cover / diffuser and locks into place the same way that this diffuser does.
I attached a little picture and then drew over to show the two pieces.
For me, it works best to insert the adaptor from behind. With the reflector lock in the "unlock" position, you can slide the large open face of the adaptor inside the center chamber from behind. Looking at the front of the unit, there are three little raised ledges inside the center chamber of the ringflash and three little raised ledges on the outside edge of the umbrella adaptor. The three ledges on the adaptor slide perfectly in between the three gaps left by the ledges inside the center chamber. You'll push the adaptor slightly forward and twist until the adaptor ledges are positioned just in front of the center chamber ledges.
You'll then place the reflector lock back in the "lock" position. When locked, the adaptor can't slide in (forwards) or out (backwards). It can still rotate slightly left and right - but not much more than about 45-degrees in either direction.
Hope this helps, let me know if you need anything else.