Integration of temporally misaligned sensory information is crucial for constructing a unified perception of our environment. Investigation into the processes facilitating temporal integration of audiovisual stimuli has uncovered that our brain adapts to compensate for cross-modal delays (i.e. temporal recalibration). Previous studies on audiovisual temporal recalibration have observed that synchrony judgement is affected by the modality order of a preceding exposure to a greater degree when vision, rather than audio, was the leading modality. This study aimed to investigate this asymmetry by considering the possibility that temporal integration of audiovisual stimuli is mediated by independent mechanisms as a function of leading modality. Here, participants responses on a simultaneity judgement task (SJ) were compared based on the modality order of a preceding trial. The stimulus used for the experiment was audiovisual alignments of the syllable /ba/. A separate mechanisms interpretation of temporal integration was supported if subjective synchrony of audio-lead and video-lead asynchronies were affected differently by the preceding modality order. The findings of this study were inconclusive. Results show that subjective synchrony judgements of audio-lead asynchronies were affected to a larger degree when the preceding modality order was audio-lead, compared to video-lead. The opposite was found for subjective synchrony of video-lead asynchronies. These findings indicate that effects of rapid temporal recalibration to audiovisual asynchronies is mediated by independent shifts of timing criteria for either modality order.