I'm sorry for the delay in answering. They are automatically added to your inventory. When you win this item on the wheel, 3 random battle items get added, so you shouldn't see the pack itself, just the spheres or potions that were in it.
I can't figure out how to claim or activate these packs when I get them. When I get a new one, it says I have 80 or something of them now. How do I unpack them to get the items?