One of two things are happening here:
This is a historical inaccuracy, either purposeful for the reason of showing why India doesn't intercede or accidental, in that someone just got the dates wrong.
The fixed points in time do not represent a point from the last scene, but rather from the last fixed point. In this case, the "Five years later, 1949" is not five years after the death of the Dalai Lama's father (the scene immediately preceding the screenshot), but rather 5 years after the prior interstitial, which begins with the car scene in 1944:
The events that unfold after this include the reference to India, as well as the Daili Lama watching video of the bombing of Japan, which was August, 1945.
I believe #2 is the correct one -- the time period of all events since the "1944" text represent not one year, but several years and the next fixed point in time references five years after 1944, not the death of his Father.