The analysis of drought onset and their potential relationship to drought severity (deficit volume) are critical for providing timely information for agricultural operations, such as cultivation planning and crop productivity monitoring. A coupling between drought timing and deficit volume can be used as a proxy for drought-related damage estimation and associated risks. Despite its high importance, so far little attention was paid to determine the timing of drought and its linkage with deficit volume for hydrological droughts. This study utilizes quality-controlled streamflow observations from 1965 to 2018 to unveil regional patterns of hydrological drought onset, trends in event-specific deficit volume, and nonlinear relationships between onset timing and deficit volume across 97 rain-dominated catchments in Peninsular India (8-24^o N, 72-87^o E). Our results show a shift towards earlier hydrological drought onset in conjunction with a decrease in deficit volume during the Indian monsoon (June-September) season, which is contrasted by a delayed onset in the pre-monsoon (March-May) and post-monsoon (October-February) seasons. Further, approximately one-third of the catchments show a significant nonlinear dependency between drought deficit volume and onset time. We find environmental controls, such as soil organic carbon, vertical distance to channel network, and soil wetness are dominant factors in influencing droughts. Our analysis provides new insights into the causal chain and physical processes linking climatic and physiographic controls on streamflow drought mechanisms, which can support drought forecasting and climate impact assessment studies.