With the widespread use of biometric authentication comes the exploitation of presentation attacks, possibly undermining the effectiveness of these technologies in real-world setups. One example takes place when an impostor, aiming at unlocking someone else's smartphone, deceives the built-in face recognition system by presenting a printed image of the user. In this work, we study the problem of automatically detecting presentation attacks against face authentication methods, considering the use-case of fast device unlocking and hardware constraints of mobile devices. To enrich the understanding of how a purely software-based method can be used to tackle the problem, we present a solely data-driven approach trained with multi-resolution patches and a multi-objective loss function crafted specifically to the problem. We provide a careful analysis that considers several user-disjoint and cross-factor protocols, highlighting some of the problems with current datasets and approaches. Such analysis, besides demonstrating the competitive results yielded by the proposed method, provides a better conceptual understanding of the problem. To further enhance efficacy and discriminability, we propose a method that leverages the available gallery of user data in the device and adapts the method decision-making process to the user's and the device's own characteristics. Finally, we introduce a new presentation-attack dataset tailored to the mobile-device setup, with real-world variations in lighting, including outdoors and low-light sessions, in contrast to existing public datasets.