When observers have to identify an object embedded in a rapid serial visual presentation (RSVP) stream, they often erroneously report the identity of a distractor instead of the target (distractor intrusion). In two experiments, we examined whether these intrusion errors are associated with the speed of attentional engagement. Participants reported the identity of target digits indicated by shape selection cues. To manipulate the speed of engagement, targets appeared either within a single RSVP stream or unpredictably in one of two streams. Objects that followed the selection cue were reported more frequently when engagement was delayed (two streams), whereas the probability of reporting objects preceding the cue was higher when engagement was faster (single stream). These results show that distractor intrusions are closely linked to the allocation of selective attention in time, making the intrusion paradigm a useful tool for research into the temporal dynamics of attention. They also provide new evidence for the idea that attentional selectivity operates within brief periods of perceptual enhancement (attentional episodes), facilitating the processing of all objects within this period, regardless of their status as targets or distractors.