Climatic fingerprint of Heinrich (H) events was characterized by widespread megadroughts over the Asian summer monsoon (ASM) region accompanied by systemic weakening of the ASM. However, recent studies of hydroclimate proxies suggest huge spatial discrepancies in precipitation over the ASM region during some H events, characterized by increased precipitation in the Yangtze River Valley contrasting with the prevalent megadroughts across the whole ASM region. The mechanism responsible for the spatial discrepancies in precipitation and the relationship between local precipitation and the ASM intensity remain elusive. In this study, we investigate the response of the ASM circulation and precipitation to orbital forcing during six H events based on simulations with a coupled atmosphere-ocean general circulation model. The results show that changes in insolation alone can induce spatial discrepancies in precipitation over the ASM region during the H events. During the H1, 3, 4, 5, 6 events, the amplification of the land-sea pressure contrast in response to a positive interhemispheric insolation gradient (30°N-30°S) during boreal summer intensifies moisture transport from the adjacent oceans to the ASM region. The ensuing moisture divergence, combined with anomalous downdrafts, results in decreased precipitation in the South Asian Summer Monsoon (SASM) region, but converse scenario for the East Asian Summer Monsoon (EASM) region. During the H2 event, the increased precipitation across the Yangtze River Valley sharply contrasts the widespread drought over the ASM region, attributing to an anticyclone anomaly over the subtropical Western North Pacific and a cyclone anomaly over Japan and Korea. Moisture budget analysis shows that the dynamic effect, especially the vertical term, rather than the thermodynamic effect, is the dominant control of precipitation changes over the ASM region. Our results also suggest that despite the synchronous variation in the strength of the EASM and SASM in response to orbital forcing, the EASM should not be regarded as an eastward and northward extension of the SASM. Furthermore, our model simulates a weak correlation between the monsoon intensity and precipitation in the SASM region in response to orbital forcing, calling for caution in employing precipitation to reconstruct SASM intensity on orbital time scale.