Not sure if this is a bug or an un-advertised limitation of the free service. If I learn on the desktop web app one day and switch to the mobile app the next day the mobile app will behave as if I didn't practice the day before. It will want me to review dozens of extra words. The same situation occurs in both directions, as if the web app and iOS app do not sync cards.
However, the statistics and trends sync perfectly between iOS and web. Also, New words learned are synced between stacks without issue. Seems as though it's just the card review data.