Federated learning has emerged as a promising privacy-preserving solution for machine learning domains that rely on user interactions, particularly recommender systems and online learning to rank. While there has been substantial research on the privacy of traditional federated learning, little attention has been paid to the privacy properties of these interaction-based settings. In this work, we show that users face an elevated risk of having their private interactions reconstructed by the central server when the server can control the training features of the items that users interact with. We introduce RAIFLE, a novel optimization-based attack framework where the server actively manipulates the features of the items presented to users to increase the success rate of reconstruction. Our experiments with federated recommendation and online learning-to-rank scenarios demonstrate that RAIFLE is significantly more powerful than existing reconstruction attacks like gradient inversion, achieving high performance consistently in most settings. We discuss the pros and cons of several possible countermeasures to defend against RAIFLE in the context of interaction-based federated learning. Our code is open-sourced at https://github.com/dzungvpham/raifle.