Incentive-based public transport demand management (PTDM) can effectively mitigate overcrowding issues in crowded urban rail systems. Analyzing passengers’ behavioral responses to the incentive can guide the design, implementation, and update of PTDM strategies. Though several studies reported passengers’ responses to fare incentives, they focused on passengers’ short-term behavioral responses. Limited studies explore passengers’ longitudinal behavioral responses for different types of adopters, which is important for policy assessment and adjustment. This paper explores and models passengers’ longitudinal behavior response to a pre-peak fare discount incentive using 18 months of smartcard data in public transport in Hong Kong. We classified adopters into six types based on their temporal travel pattern changes before and after the promotion. The longitudinal analysis reveals that among all adopters, 19% of users change their departure times to take advantage of fare discounts but do not contribute to the goal of reducing peak-hour travel. However, these adopters are more likely to sustain their changed behavior in a long term which is not desired by the incentive program. The spatial analysis shows that the origin station distribution of late adopters is relatively more diverse than the early adopters with more trips starting from distant areas. The diffusion modeling shows that the majority adopters are innovators and the word-of-mouth diffusion effect (imitators) is marginal. The discrete choice model results highlight the heterogeneous impact of factors on different types of adopters and their values of time changes. The significant factors common to adopters are: departure time flexibility, the expected money savings, the required departure time changes, and work locations. The findings are useful for public transport planners and policymakers for informed incentive design and management.