If your decks do not show in the iPhone app, please follow these steps
The first time you open a deck on your iPhone it is downloaded from iCloud to your phone. Once downloaded, you can study your cards as usual. The next time your iPhone is connected to the Internet, your study progress is uploaded back to iCloud and your Mac.
Please note that you need either the full version of the Mac app or the free version with the In-App purchase of the full version to be able to use the iPhone app.