Rainfall-runoff models are frequently used for assessing climate risks by predicting changes in streamflow and other hydrological processes due to anticipated anthropogenic climate change, climate variability, and land management. Historical observations are commonly used to calibrate empirically the performance of conceptual hydrological mechanisms. As a result, calibration procedures are limited when extrapolated to novel climate conditions under future scenarios. In this paper, rainfall-runoff model performance and the simulated catchment hydrological processes were explored using the JAMS/J2000 model for the Berg River catchment in South Africa to evaluate the model in the tails of the current distribution of climatic conditions. An evolutionary multi-objective search algorithm was used to develop sets of parameters which best simulate “wet” and “dry” periods, providing the upper and lower bounds for a temporal uncertainty analysis approach to identify variables which are affected by these climate extremes. Variables most affected included soil-water storage and timing of interflow and groundwater flow, emerging as the overall dampening of the simulated hydrograph. Previous modeling showed that the JAMS/J2000 model provided a “good” simulation for periods where the yearly long-term mean precipitation shortfall was <28%. Above this threshold, and where autumn precipitation was reduced by 50%, this paper shows that the use of a set of “dry” parameters is recommended to improve model performance. These “dry” parameters better account for the change in streamflow timing of concentration and reduced peak flows, which occur in drier winter years, improving the Nash-Sutcliffe Efficiency (NSE) from 0.26 to 0.60 for the validation period 2015–2018, although the availability of climate data was still a potential factor. As the model performance was “good” (NSE > 0.7) during “wet” periods using parameters from a long-term calibration, “wet” parameters were not recommended for the Berg River catchment, but could play a large role in tropical climates. The results of this study are likely transferrable to other conceptual rainfall/runoff models, but may differ for various climates. As greater climate variability drives hydrological changes around the world, future empirically-based hydrological projections need to evaluate assumptions regarding storage and the simulated hydrological processes, to enhanced climate risk management.