No, there are no special storage instructions for the Supersoft items. Full disclosure - I am a terrible toy collector, and mine are chucked haphazardly in their storage case. I also have a number of supersoft prototypes in my office on a shelf, and none have ever lost their shape.
The only caution I give people is that we have had instances where the black lining of a storage case (specifically made for sex toys, BTW) was waterproofed with something that discolored the toy. I had a very upset customer whose Vamp got blotchy after being stored in this particular case, so while I am not worried about the position of Tantus toys, I would use some caution in choosing where to to store them. Hope that helps! And enjoy your new Supersoft VIP