The information used by conscious perception may differ from that which drives certain actions. A dramatic illusion caused by an object's internal texture motion has been put forward as one example. The motion causes an illusory position shift that accumulates over seconds into a large effect, but targeting of the grating for a saccade (a rapid eye movement) is not affected by this illusion. While this has been described as a dissociation between perception and action, an alternative explanation is that rather than saccade targeting having privileged access to the correct position, a shift of attention that precedes saccades resets the accumulated illusory position shift to zero. In support of this possibility, we found that the accumulation of illusory position shift can be reset by transients near the moving object, creating an impression of the object returning to near its actual position. Repetitive luminance changes of the object also resulted in reset of the accumulation, but less so when attention to the object was reduced by a concurrent digit identification task. Finally, judgments of the object's positions around the time of saccade onset reflected the veridical rather than the illusory position. These results suggest that attentional shifts, including those preceding saccades, can update the perceived position of moving objects and mediate the previously reported dissociation between conscious perception and saccades.