Research has shown that children on the autism spectrum and adults with high levels of autistic traits are less sensitive to audiovisual asynchrony compared to their neurotypical peers. However, this evidence has been limited to simultaneity judgments (SJ) which require participants to consider the timing of two cues together. Given evidence of partly divergent perceptual and neural mechanisms involved in making temporal order judgments (TOJ) and SJ, and given that SJ require a more global type of processing which may be impaired in autistic individuals, here we ask whether the observed differences in audiovisual temporal processing are task and stimulus specific. We examined the ability to detect audiovisual asynchrony in a group of 26 autistic adult males and a group of age and IQ-matched neurotypical males. Participants were presented with beep-flash, point-light drumming, and face-voice displays with varying degrees of asynchrony and asked to make SJ and TOJ. The results indicated that autistic participants were less able to detect audiovisual asynchrony compared to the control group, but this effect was specific to SJ and more complex social stimuli (e.g., face-voice) with stronger semantic correspondence between the cues, requiring a more global type of processing. This indicates that audiovisual temporal processing is not generally different in autistic individuals and that a similar level of performance could be achieved by using a more local type of processing, thus informing multisensory integration theory as well as multisensory training aimed to aid perceptual abilities in this population.