Sensorimotor synchronization to external events is fundamental to social interactions. Adults with autism spectrum condition (ASC) have difficulty with synchronization, manifested in both social and non-social situations, such as paced finger-tapping tasks, where participants synchronize their taps to metronome beats. What limits ASC's synchronization is a matter of debate, especially whether it stems from reduced online correction of synchronization error (the "slow update" account) or from noisy internal representations (the "elevated internal noise" account). To test these opposing theories, we administered a synchronization-continuation tapping task, with and without tempo changes. Participants were asked to synchronize with the metronome and continue the tempo when it stopped. Since continuation is based only on internal representations, the slow update hypothesis predicts no difficulty, whereas the elevated noise hypothesis predicts similar or enhanced difficulties. Additionally, tempo changes were introduced, to assess whether adequate updating of internal representations to external changes is possible when given a longer temporal window for updating. We found that the ability to keep the metronome's tempo after it stopped did not differ between ASC and typically developing (TD) individuals. Importantly, when given a longer period to adapt to external changes, keeping a modified tempo was also similar in ASC. These results suggest that synchronization difficulties in ASC stem from slow update rather than elevated internal noise.