The pulse of the climate (cold to warm to cold to warm etc) seems to have been the large reason for the migration down the steppe, probably in both directions.
Now they were a pretty organized and aggressive society at the time (kept up with the Chinese in technology) so from their base in Bhutan they moved out into india proper well enough that they show up as one of the fighting factions in the Mahabarat.
They maintained contact with Yakutia (currently the largest subdivision of Russia in Siberia) with trade routes all over the place ~ and a big connection into what we today call The Silk Road.
When the climate got cold they moved much of their nation South to India. When it warmed up, or the Indians got restive (see 200AD) they moved the nation North.
About 560 AD they MOVED EAST to Korea, and then Japan. I gather that climate anomaly was a humdinger. Killed off all their people who knew the ancient language in which their records were kept. They've recently been interpreted by Russian archaeologists.
I didn't know there was solid evidence for this 7th century BC cold spell, but everybody figured there had to be one since so terribly many settled populations pulled up stakes and went somewhere else!