Yes I experienced that, but the only difference is I use to fake the accent at times, when I moved from India to UK, I was young and started talking like others, however, sometimes, I use to do it deliberately just for fun, or to look cool. Then I returned back to India and went to the States after four years, there I did not fake the accent, I was myself. I guess the change of accent only happens when one has lived in the country over nine to ten years or more I believe.