The summer rainfall climate of East Asia underwent large and abrupt changes during past climates, in response to precessional forcing, glacial-interglacial cycles as well as abrupt changes to the North Atlantic during the Last Glacial. However, current interpretations of said changes are typically formulated in terms of modulation of summer monsoon intensity, and do not account for the known complexity in the seasonal evolution of East Asian rainfall, which exhibits sharp transition from the Spring regime to the Meiyu, and then again from the Meiyu to the Summer regime.We explore the interpretation that East Asian rainfall climate undergoes a modulation of its seasonality during said paleoclimate changes. Following previous suggestions we focus on role of the westerly jet over Asia, namely that its latitude relative to Tibet is critical in determining the stepwise transitions in East Asian rainfall seasons. In support of this linkage, we show from observational data that the interannual co-variation of June (July-August) rainfall and upper tropospheric zonal winds show properties consistent with an altered timing of the transition to the Meiyu (Summer), and with more northward-shifted westerlies for earlier transitions. We similarly suggest that East Asian paleoclimate changes resulted from an altered timing in the northward evolution of the jet and hence the seasonal transitions, in particular the transition of the jet from south of the Plateau to the north that determines the seasonal transition from Spring rains to the Meiyu. In an extreme scenario - which we speculate the climate system tended towards during stadial (cold) phases of D/O stadials and periods of low Northern Hemisphere summer insolation - the jet does not jump north of the Plateau, essentially keeping East Asia in prolonged Spring conditions. We argue that this hypothesis provides a viable explanation for a key paleoproxy signature of D/O stadials over East Asia, namely the heavier mean δ18O of precipitation as recorded in speleothem records. The southward jet position prevents the low-level monsoonal flow - which is isotopically light - from penetrating into the interior of East Asia; as such, precipitation there will be heavier, consistent with speleothem records. This hypothesis can also explain other key evidences of East Asian paleoclimate changes, in particular the occurrence of dusty conditions during North Atlantic stadials, and the southward migration of the Holocene optimal rainfall.