That was the Khazars, not the Mongols. And the Pechenegs after the Khazars. And then the Rus' had to deal with the Cumans and the Kipchaks. The Mongols only arrived after them.

The steppes were full of nomadic and semi-nomadic peoples. For thousands of years, various powers rose and fell, and sometimes they set out to conquer the surrounding sedentary peoples. The Mongols were just one of the more successful ones. (But arguably not the most successful, as the Proto-Indo-Europeans probably also came from the steppes.)