It was not only because of the Russian Civil War or the Prohibition which made vodka a special deal in the US in the 1920s. It was simply that it wasn't an easily acquirable item because there wasn't really a big market for it. The liquor preference in the US at the time was whiskey/bourbon and rum, so most other liquors would not be commonly available.
Victorino Matus the author of Vodka: How a Colorless, Odorless, Flavorless Spirit Conquered America (2014) makes the claim that it was actually the prohibition that created the foundation for vodka (and other spirits) to become popular in the US, in that during that period people became used to drinking all sorts of stuff as long as it had alcohol, and so the cultural preference for whiskey and rum eroded. So in the following decades other liquors gradually entered the market, vodka became popular during the 1940s and 1950s, and it eventually ended up becoming the most popular liquor in the US.