It was largely immigration, during that period. It self-perpetuated through natural birth, but the initial impetus was immigration and that picked up as anti-Semitism did, particularly while Jews fled Europe and the rise of the Nazis in the early to mid 1930s.

There are other examples of groups doing this though I can't think of any indigenous population returning to their homeland quite like that. Israel actually provides an example of that. In the 1990s, after the fall of the Soviet Union, over 1 million Russian Jews arrived in Israel. Most of them arrived between 1989 and 1998, during which time around 700,000 arrived. They went from less than 5% of the population to over 15%.

A similar situation happened in Israel post-1948. The fledgling Jewish state of roughly 750,000, around 600,000 or so of them Jews, began taking in huge amounts of Jews from Arab states (as well as European Jews from displaced persons camps). The Jews from Arab states made a significant shift in the up-til-then mostly European Jewry that lived in Israel. Mizrahi (at least part-Mizrahi) citizens (those with ancestors from Arab states) by 1998 made up a majority of Israel's Jewish population, if memory serves. The Israeli population virtually doubled in the first 5 years of its existence, and Mizrahi Jews went from being a small percentage of the population to being well over a quarter, if not a third, of the population.