Localized tropical rainfall changes commonly occur on 500-1,000 km scales under many climate forcings, but understanding their causality is notoriously challenging. One helpful process-oriented diagnostic (POD) decomposes the effects of undilute buoyancy and mid-level moisture through a precipitation-buoyancy relationship, but its applicability at these scales is uncertain. In this context, we examine month-to-month changes in five subregional "hotspots" of the South Asian monsoon. While the POD qualitatively explains month-to-month rainfall, revealed variability in the precipitation-buoyancy relationship leads to underprediction of rainfall changes by 18-90%. Encouragingly, in a subset of subregions with minimal variability, the POD successfully identifies how shifts in the large-scale thermodynamic environment drive rainfall changes, highlighting the role of mid-level moisture in modulating monsoon onset. We encourage the same methodology be broadly applied to interpret thermodynamic drivers of similarly localized precipitation changes that occur in climate model predictions of warming, aerosol effects, geoengineering, and ENSO.