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Kolkata lies more west than where Shillong lies.In simple words,Shillong lies east to Kolkata and so falls first in the path of Bay of Bengal branch of South west monsoon.
The general trend of Bay of Bengal monsoon winds that cause rainfall in eastern part of India is from east to west along the Ganga valley over northern plains of the country.

As Shillong is situated on the eastern side of Kolkatta,the precipitation occurs first(in the month of June) and then Kolkata(sharply in the month of July)