Not to split hairs, but I don't think AA will be "taking over" the Aviators accounts on July 3rd. However, Amex has said it will end its relationship with Aviators at that time.
So, yes, you will have to open an Aviators account if you don't have one (you can probably do that online), then tranfer your Amex points by July 3.
Eventually, AA will absorb Aviators. You'll just have to let your newly-tranferred points sit until they do.