The summer monsoon onset over the Bay of Bengal and South China Sea signals the beginning of the Asian summer monsoon, critical for local fisheries, agriculture and livelihoods, so communities are concerned about its potential changes under global warming. Previous projections have suggested a delay, but the extent of this delay remains uncertain, undermining the reliability of the projections. Here, we show a significant correlation between the projected shift in Bay of Bengal/South China Sea monsoon onset and present‐day sea surface temperature (SST) simulation over the western Pacific (WP). This emergent relationship arises from the spread of the precipitation response over the western‐central Pacific to WP SST, as more precipitation induces stronger tropical upper‐tropospheric warming, increasing westerly vertical shear near South Asia, and facilitating the onset delay. The rectified projections indicate that the delayed shift is almost halved compared to raw projections, and the intermodel uncertainty is reduced by 30%.