This whole partition thing was a clumsy mess.
Even after the creation of Pakistan and India,there were still hundreds of princely states existing within the present political boundaries of India.
So,if the question is about the Domino status,then,technically India got rid of it when it got her independence,but the integration of some of the princely states took some more time and gave the shape the India presently has.
Apart from the princely states,there were French colonies,Portuguese colonies etc.,some of which were integrated as late as 1961.Now depending upon the perspective,some may call it integration and some may call it annexation,does not make any difference though in the present scenario.
After the independence,the post of Viceroy was replaced by the post of Governor General.It was because of the transition of a centuries old colony in to an independent nation.
There were still many princely states which were loyal to the British crown but did not have any official loyalty declared towards India.So,a supervisor was necessary.There was no foreign policy devised at that time,as these things tend to take a lot of time.Lord Mountbatten was the first Governor General,subsequently replaced by C.Rajagopalachari.When the Indian Constitution was drafted in 1950,the post of Governor general was not required any more,and it was abolished.Instead the post of President of India was created.
Hope this answers the question.
p.s. : An incomplete list of Princely states of India can be found
here . It contains only the bigger states and not many smaller ones.