When you buy something from the Sims Store, sometimes you need to tell your browser to download it into The Sims 3 Download folder. This folder is located "Documents > Electronic Arts > The Sims 3 > Downloads". When you officially download the item, it still needs to be installed via the Launcher into the game. You do this by choosing the item and hitting the install button from the downloads section of your launcher.
Then when you enter the game, the aquarium still has to be purchased by your Sims to be placed into their house.