It seems to me the origin of the monsoons is attributed to the Himalayas: The massive mountains blocked the global air circulation pattern with the formation of the peculiar monsoons (local word which means "seasonal").
Air moves from the north in the winter and then it reverses in the summer.
Both plate of Himalayan and Tibet were parallel to the most extreme and unstable of fault line underneath earth crust i.e. Australasia-Burma-Hindi which too closer. I believe these plateau has strongly correlated on what monsoonal effect became stumble and vulnerably as well as climate impacted through atmospheric breakdown hitherto and upcoming.
Agree with the Gregore opinion. As Michael said the massive mountains already act as a barrier and prevent to cross the global prevailing winds from one side of mountains range to other side (both summer and winter seasonal winds). This barrier in fact helps to form the famous SW monsoon in the subcontinent. Thus slight geological uplifting of mountains may not have any significant impact on SW (summer) and NE (winter) monsoons in the region.