Understanding onset of droughts and its potential linkage to resulting responses like severity (deficit volume) is crucial for providing timely information related to drought sectors including the cultivation planning and monitoring crop productivity. Using high-quality daily observed streamflow records from 82 medium-to-large sized catchments over (tropical) peninsular India, we show that the variability in onset timing drives the severity of hydrological droughts. The strength of onset timing-severity relationships using observed records indicate seasonality of rainfall and catchment characteristics mainly modulate hydrological drought responses in peninsular India, which is not readily apparent from land-surface model simulations. The observed trend for mean onset of drought depicts delayed occurrence for more than half of the catchments. Around one-third of the catchments shows a stronger non-linear significant dependency (>0.7) between severity and onset of drought. The findings of the study highlight the need for accounting feedback between drought onset and severity and their concurrent changes for seasonal-to-sub-seasonal predictability of droughts; and contributes to discussions on building resilience to extreme droughts in a changing climate.