Fiddler on the Roof is the story of a fictional Jewish town, known as a shtetl, in the Pale of Settlement of Imperial Russia. For the most part, the majority of the residents had been living in the area for generations, since the Pale was mostly made up of former territories of Poland-Lithuania Commonwealth (mostly present day Belarus and Ukraine). The Pale was created as an area in Imperial Russia where Jews could live, at first it was a relatively small area of western Russia, it grew as the borders of Russia expanded into the Commonwealth. Even inside of the Pale there were limits on where Jews could live, resulting in the majority residing in Jewish-only settlements.

As to the reasons, there are myriad. While these areas were traditionally more tolerant to Jews than much of Europe, tension between Christian and Jewish communities still existed. During this period Russian policy was very anti-Semitic and tried to force convert or expel the entire Jewish population. Once these territories were under Russian control, tension between the two religious communities grew, unfettered and often inflamed by the authorities. In addition to all of this, due to the influx of expelled Jews from the interior of Russia with few possessions and wealth and a high level of poverty in the Jewish towns, petty crime in Christian communities was blamed on Jews.

Source: A History of East European Jews

FWIW, I've never heard of expulsions in Imperial Russia, and expelling Jews from a small village doesn't make a whole lot of sense. At this point Jews were restricted to a specific geographic area (the Pale of Settlement). While chasing the Jews out of town via a pogrom was not uncommon, doing so in a small town via a law is a bit strange.

However, and it is a big however, not only does this take place in the movie but it takes place in the original book by Sholem Aleichem, who was writing at the same time and in the same place (more-or-less) as the story is set. Which indicates that even if this specific thing didn't happen, it was at the very least it was a believeable plot device for Sholem Aleichem himself (and presumably his audience, who also lived in the same place and at the same time as the story is set).

Were the Jewish residents new to that region? Or had they migrated there generations earlier?

No, there'd been a large Jewish community in Eastern Europe for several centuries by that point.

What was the reason for the expulsion of a non-militant population?

I think this part of it is a bit....naive? maybe? It's hard to explain prejudice, I guess. People kicked Jews out of their towns, attacked them, restricted them legally, and used laws to fragment communities, because they could. Some of it was definitely religious prejudice, but for the most part discrimination was how societies worked. They didn't need a reason, really. That's not to say the discrimination in general was totally unexplained--there were all sorts of conspiratorial beliefs floating around that would often precipitate violence. But there's no real reason for those, either. Some societies simply have discrimination against a particular group as a thing people just do, and Eastern Europe in the 19th century was one of them.