East Asian migration to Europe made a full 5% impact on ALL European populations. With small populations, the migration of a few mighty hunters, or the importation of a beautiful woman could have a massive impact.
The Huns added a very negligible amount ~ same for the Mongols, etc.
And while it's true that a small migration can leave a larger genetic footprint on a small population, a relatively small group of military conquerers can leave a fairly large genetic footprint. A team of geneticists claim that 1 in 12 men in Asia carry a Y chromosome mutation that originated in Mongolia 1,000 years ago, the legacy of Genghis Khan's conquests.