In case of delayed visual feedback during visuomotor tasks, like in some sluggish computer games, humans can modulate their behavior to compensate for the delay. However, opinions on the nature of this compensation diverge. Some studies suggest that humans adapt to feedback delays with lasting changes in motor behavior (aftereffects) and a recalibration of time perception. Other studies have shown little or no evidence for such semipermanent recalibration in the temporal domain. We hypothesize that predictability of the reference signal (target to be tracked) is necessary for semipermanent delay adaptation. To test this hypothesis, we trained participants with a 200 ms visual feedback delay in a visually guided manual tracking task, varying the predictability of the reference signal between conditions, but keeping reference motion and feedback delay constant. In Experiment 1, we focused on motor behavior. Only training in the predictable condition brings about all of the adaptive changes and aftereffects expected from delay adaptation. In Experiment 2, we used a synchronization task to investigate perceived simultaneity (perceptuomotor learning). Supporting the hypothesis, participants recalibrated subjective visuomotor simultaneity only when trained in the predictable condition. Such a shift in perceived simultaneity was also observed in Experiment 3, using an interval estimation task. These results show that delay adaptation in motor control can modulate the perceived temporal alignment of vision and kinesthetically sensed movement. The coadaptation of motor prediction and target prediction (reference extrapolation) seems necessary for such genuine delay adaptation. This offers an explanation for divergent results in the literature.