Q -

Did you look that up just for the sake of argument (to split hairs - "there was a war"), or do you really think it has some bearing on this?

Just because I don't write every detail, it doesn't mean I am not aware of them.

The details being as they are, it doesn't make sense to refer to "the war of '47" (nobody says that), nor would the father character in the song have likely left "the Poonjab" (Punjab) then; he would have relocated to the "other side". (to Eastern Punjab if he was Sikh or Hindu; to western Punjab if he was Muslim). The lyric in the song makes it as though Partition was a war, and that it forced people out of that whole part of the world. (People involved in the Partition's uprootment don't say they "left Punjab"; they say we came to this side or that.) Further lyrics make it sound as if the father's family had some faith-driven reason for needing to strike out in new parts of the word, whereas the only "religious" reason had nothing to do with belief, but rather the religious community (however nominally) to which you belonged - the fact that Pakistan would be an Islamic state.
In short, the author has taken a vague knowledge of the events and reimagined the details and the motivations, probably according to other models (e.g. emigration of Vietnamese to U.S. after Vietnamese conflict).