Attention, or more generally, driver monitoring systems have been identified as a necessity to address overreliance on driving automation. However, research suggests that monitoring systems may not be sufficient to support safe use of advanced driver assistance systems (ADAS), also evidenced by a recent major recall of Tesla’s monitoring software. The objective of the current study was to investigate whether different training approaches improve driver behaviour while using ADAS with an attention monitoring system. A driving simulator study was conducted with three between-subject groups: no training, limitation-focused training (highlighted situations where ADAS would not work), and responsibility-focused training (highlighted the driver’s role/responsibility while using ADAS). All participants (N = 47) experienced eight events which required the ego-vehicle to slow down to avoid a collision. Anticipatory cues in the environment indicated the potential for the upcoming events. Event type (covered in training vs. not covered) and event criticality (action-necessary vs. action-not-necessary) were within-subject factors. The responsibility-focused group made fewer long glances (≥ 3 s) to a secondary task than the no training and limitation-focused groups when there were no anticipatory cues. Responsibility-focused training and no training were associated with faster takeover time at the events than limitation-focused training. There were additional benefits of responsibility-focused training for events that were covered in training (e.g., higher percent of time looking at the anticipatory cues). Overall, our results suggest that even if attention monitoring systems are implemented, there may be benefits to driver ADAS training. Responsibility-focused training may be preferable to limitation-focused training, especially for situations where minimizing training length is advantageous.