Until 1989 the Ukraine was, of course, a part of the Russian Empire. Most Jews who came from the Ukraine to the US came either from the region of Odessa, in the Southern Ukraine, a Turkish posession until 1789 when Catherine the Great conquered it, or else Volhynia (a province immediately East of Austrian Galitzia, in the "Polish" Ukraine), which Catherine obtained at the Third Partition of Poland in 1795.
Thus a vast majority of the world's Ashkenazy Jews came under the absolute rule of a German Princess in a country where, before, there had hardly been any Jews at all. It was Catherine who instituted all the legal and geographical limitations on Jewish life that drove millions of them to leave her realms.
Originally, she had been a very minor German princeling named Sophie von Anhalt-Zerbst. She adopted the name Yekaterina Alekseyevna when she married the heir to the Russian throne at age 15 in 1744. Six months after he inherited the Imperial crown, she staged a coup, had him killed, and usurped the thone, ruling as Tsarina for 34 years.
Although she posed as an Enlightened Despot, like her fellow German "enlightened" despot, Frederick The Great, she hated Jews. They saw them as hoarders, masters of financial skullduggery, physically useless as soldier material, and politically unreliable.
Later, anti-Russian rhetoric from Jews who had emigrated West, and the embrace of subversive organisations by Jews remaining in Russia, only made things worse.