The online, International Encyclopedia of the First World War places the numbers at around 1 to 1.3 million Russian émigrés scattered around the world by 1921, when the Civil War was all over but the crying. That figure appears reasonable to me, I have seen up to 2 million. It is exceptionally different to get a precise number, as Russians fled to many different places and not all at the same time. Paris and Harbin, in China, were the two great clusters of post-war White Russian life.

You might be interested in checking out Richard Pipes' Russia under the Bolshevik Regime - it has quite a good section on the Russian Civil War and he may cover this in more detail, but I forget the book on my last move so I'm kicking myself that I can't answer your question more fully.