Antisemitism has a long history in Eastern Europe, going back way further than Communism. But the basis for it was religious and political rather than the systematic racial antisemitism of the Nazis. You're missing that distinction, and its consequences in terms of how the killing was organized.
The above reflects the common error that there was some sort of essential difference between the anti-Jewish ideology of German National Socialism and the judeophobia that was so wide-spread Eastern Europe.
Detailed investigation of the early history of the German National Socialist movement and Hitler's involvement, especially in the years from 1919 to the Putsch in November 1923, has shown conclusively that the anti-Jewish ideology of Hitler and the National Socialist movement was derived from right-wing Russian exiles who had settled in Germany after fleeing from Bolshevik rule in their homeland.
Those Russian exiles had been anti-Semitic in outlook before the First World War, and their anti-Semitism had a variety of historical causes, some religious, some cultural and economic, some apocalyptic and occult. Their anti-Jewish ideology had been given form in pareticular by the Russian writer, Dostoevskii. However, their anti-Semitism had been greatly intensified by their experience of the Russian Revolution; they blamed Jews for both the overthrow of the Tsar in march 1917 and the subsequent Bolshevik takeover in November of that year. They saw the Bolshevik regime as essentially Jewish, and an attempt by the Jews to exterminate the best elements of the Russian people, by starvation in particular, for the purpose of establishing a Jewish dictatorship over the lower classes of the former Russian Emp[ire.
That ideology was imparted by the exiles to right-wing völkisch movements in Germany, including to the nascent National Socilaist movement. Hitler himself had not professed an anti-Semitic ideology prior to 1919, being more a Socialist by inclination; he acquired that ideology under the influence of ethnic German exiles from Russia, Alfred Rosenberg and Max Erwin von Scheubner-Richter (the latter served as Hitler's primary political adviser until he was killed in the November 1923 Putsch).
Once Hitler had acquired his anti-Semitic ideology from the Russian exiles, the main message preached by him (in addition to his previous main message that the Versailles sustem must be overthrown) was that the Jews in Germany were plotting to bring about the same sort of Bolshhevik revolution that had occurred in Russia, with all the attendant atrocities, including the extermination of the German ruling class. Hitler preached that the Jews must be expelled from germany in oder to protect the German people from the same disaster that had befallen the Russian people.
This anti-Bolshevik ideology is still apparent in his book "Mein Kampf", written in 1924 and 1926, after the influence of the Russian exiles had begun to fade.
A good book to read on the influence of the Russian exiles and the source of the anti-Semitic ideology of the national Socialist movement and of Hitler personally is:
"The Russian Roots of Nazism: White Emigres and the Making of National Socialism, 1917-1945", by Michael Kellogg (Cambridge University Press, 2005).
One particular quote from the writings of Dostoevskii that was used by the Russian exiles, and also by Alfred Rosenberg, the ideologist of the National Socialist movement, was this passage from "Diary of a Writer", dated March 1977:
Their empire is drawing near, their entire empire! The triumph of the Jews is nearing, before which brotherly love, the truth, Christian sentiments, and the national pride of the European peoples will fade and recede.
For example, the passage was quoted in an article, "Dostoevskii (born 1921) and the Jewish Question" in the 14 July 1921 edition of "Der Nationalsozialist" (a replacement periodical for the temporarily outlawed "Völkischer Beobachter, the main National Socialist newspaper). It also quoted this further passage from Dostoevskii's work:
What would happen if there were three million Russians and 80 million Jews in Russia instead of the other way around, what would the latter do with the Russians, how would they handle them?.... Would they not simply make them into slaves? Or worse yet, would they not skin them completely? Would they not exterminate them entirely, not destroy them just as they had other peoples earlier in their ancient history?
In the above passage, the impulse for the anti-Jewish ideology of National Socialism, and for the later attempt to physically exterminate the Jewish populations under German control, is transparent.
There was another article about Dostoevskii in the "Völkischer Beobachter" edition of 27 January 1923, "Dostoevskii as Politician and Prophet", which quoted from a passage of Dostoevskii's that was first published in an anniversary edition of "Diary of a Writer" in 1906. Dostoevskii had asserted: "When the entire wealth of Europe has been wasted, the bank of the Jew will remain. Then the Anti-Christ may come and anarchy rule".
The article commented on Dostoevskii's warning as follows:
Anarchy already rules in Russia today ......Russia ignored the admonitions of Dostoevskii and so the poet of yesterday will become the poet of the Russia of tomorrow, which with its return to the völkisch will have found its way home out of anarchy. For the rest of Europe, however, Dostoevskii is still the poet and admonisher for today, for perhaps already tomorrow "may the Anti-Christ come and anarchy rule".
What the above demonstrates is that the anti-Jewish ideology of National Socialism drew on traditional religious motifs, such as that of the Anti-Christ, which had been at the basis of Dostoevskii's own judeophobia.
Dostoevskii also originated the idea that Jews were the manipulators of both capitalism and communism, an idea adopted by Rosenberg and transmitted by him to Hitler.
Thus, when German forces invaded the Soviet Union in 1941, they were entering the land and encountering the people from which their own anti-Jewish ideology had been derived. It is no accident that the German massacre of Jewish minorities began in earnest when Germans entered that land, where alleged Jewish Bolshevism had originated and erected a supposed reign of terror over a gentile population. There was no essential difference between the anti-Jewish ideology of German National Socialism and the strong anti-Jewish feelings of some populations in the Soviet Union, particularly in Ukraine.