When you go home because your state is falling apart and you consequently suffer an embarassing military defeat from your former fuckboys, that counts as being kicked out.
No it doesn't, being kicked out counts as kicked out, going home counts as going home.
Mongolians show up, conquer the Russian principalities, burn down their cities and enslave their people then go home to select a new leader. Then when the Mongolian Empire splits into its successor Empire, the Golden Horde turkic Mongols still maintain their yoke on the Russians. It is noteworthy that after their defeat by their fuccbois at Kulikovo, they assembled their entire horde to devastate the lands and burn Moscow to the ground again, forcing the Russians to accept their suzerainty all over again. The man to thank for Russians being free of Mongols is another Mongol, Timur, founder of the Timurid Empire, who took vast tracts of the Golden Horde's lands, people and deported all of their artisans and craftsmen to central Asia, terminating the Golden Horde's access to the silk road, their technological advancement and their manpower.
Famines were part of why the empire fell, but yeah, looks like temperatures dropped about 1 degree around the 2st century. Honestly that wouldn't have had much of an effect if food from Egypt and Africa had kept flowing, but coupled with the massive political instability, shit was going to happen eventually.
Also food production was not terminated in northern Europe, the Germanic tribes actually grew greatly in population causing them to be an even greater threat to the Roman Empire, at the same time that plagues terminated the Med trade and made Roman provinces seek to be self sufficient rather than dependent on plague trade. Good time for agriculture