Digital tracing alerts have emerged as an effective means to share information with agility in responding to disaster outbreaks. Governments are able to instantaneously coordinate the available information to provide information related to the disaster and promote preventive actions. However, despite the opportunities granted by these innovative technologies in managing disasters, privacy concerns can arise regarding how much of individuals' private information should be collected and disclosed. With these considerations, we examine the extent to which instant digital tracing alerts and the information included in the alerts affect people's actions toward disaster management in the context of South Korea. We leverage 4,029,696 subdistrict and hour level data set, including population movement and digital tracing alert transmission information. Our results show that digital tracing alerts are effective in inducing population movement out of the infected area and decreasing the population density. Specifically, instant messaging induces movement among 2.45% of an infected district's population to other administrative areas in a given hour and decreases population density by 3.68%. Furthermore, the effectiveness of digital tracing alerts hinges on the inclusion of different private information of individuals on case confirmation. We find the heterogeneous effect of digital alerts, with the effects being more pronounced among young and male individuals and in business-centric areas. Further analysis reveals that digital tracing alerts are particularly effective at the early stage of the disaster. In addition, sending more than three messages within a day has a valid counter-effect (i.e., fatigue effects), whereas messages sent when the cumulative number of confirmed cases is high exert a less positive effect than when the verified cases are low (i.e., desensitization effects). Our results provide policy makers and law enforcement with novel insights into whether and how the use of information technology can facilitate disaster management and to what extent they should collect and expose private information to effectively safeguards public health and safety during a crisis.