People emigrating from the countries of Eastern Europe has been going on for centuries. Not since the population movements of the later middle ages has their been net immigration into the wider region.
With the growing dominance of Western European culture and economy, outmigration has been steady, sometimes frantic (including people fleeing persecutions, like pogroms).
Only recently with many E. European countries coming ever closer to Western economic systems (as in the Baltics, Poland, Chechia, Ukraine, and others, but notably not Russia) has their been a diminution and even reversal of these migratory patterns.
The current crisis will reinforce outflows from Russia and reverse inflows into Ukraine (depending on how this finally ends). Even now the regular flow of Russian outmigration has sped up in the last few days.