Conditional automated driving [level 3, Society of Automotive Engineers (SAE)] requires drivers to take over the vehicle when an automated system’s failure occurs or is about to leave its operational design domain. Two-stage warning systems, which warn drivers in two steps, can be a promising method to guide drivers in preparing for the takeover. However, the proper time intervals of two-stage warning systems that allow drivers with different personalities to prepare for the takeover remain unclear. This study explored the optimal time intervals of two-stage warning systems with insights into the drivers’ neuroticism personality. A total of 32 drivers were distributed into two groups according to their self-ratings in neuroticism (high vs. low). Each driver experienced takeover under the two-stage warning systems with four time intervals (i.e., 3, 5, 7, and 9 s). The takeover performance (i.e., hands-on-steering-wheel time, takeover time, and maximum resulting acceleration) and subjective opinions (i.e., appropriateness and usefulness) for time intervals and situation awareness (SA) were recorded. The results showed that drivers in the 5-s time interval had the best takeover preparation (fast hands-on steering wheel responses and sufficient SA). Furthermore, both the 5- and 7-s time intervals resulted in more rapid takeover reactions and were rated more appropriate and useful than the 3- and 9-s time intervals. In terms of personality, drivers with high neuroticism tended to take over immediately after receiving takeover messages, at the cost of SA deficiency. In contrast, drivers with low neuroticism responded safely by judging whether they gained enough SA. We concluded that the 5-s time interval was optimal for drivers in two-stage takeover warning systems. When considering personality, drivers with low neuroticism had no strict requirements for time intervals. However, the extended time intervals were favorable for drivers with high neuroticism in developing SA. The present findings have reference implications for designers and engineers to set the time intervals of two-stage warning systems according to the neuroticism personality of drivers.