Many behaviourally relevant sensory events such as motion stimuli and speech have an intrinsic spatio-temporal structure. This will engage intentional and most likely unintentional (automatic) prediction mechanisms enhancing the perception of upcoming stimuli in the event stream. Here we sought to probe the anticipatory processes that are automatically driven by rhythmic input streams in terms of their spatial and temporal components. To this end, we employed an apparent visual motion paradigm testing the effects of pre-target motion on lateralized visual target discrimination. The motion stimuli either moved towards or away from peripheral target positions (valid vs. invalid spatial motion cueing) at a rhythmic or arrhythmic pace (valid vs. invalid temporal motion cueing). Crucially, we emphasized automatic motion-induced anticipatory processes by rendering the motion stimuli non-predictive of upcoming target position (by design) and task-irrelevant (by instruction), and by creating instead endogenous (orthogonal) expectations using symbolic cueing. Our data revealed that the apparent motion cues automatically engaged both spatial and temporal anticipatory processes, but that these processes were dissociated. We further found evidence for lateralisation of anticipatory temporal but not spatial processes. This indicates that distinct mechanisms may drive automatic spatial and temporal extrapolation of upcoming events from rhythmic event streams. This contrasts with previous findings that instead suggest an interaction between spatial and temporal attention processes when endogenously driven. Our results further highlight the need for isolating intentional from unintentional processes for better understanding the various anticipatory mechanisms engaged in processing behaviourally relevant stimuli with predictable spatio-temporal structure such as motion and speech.