That map is misleading. We know from history that the 2nd group didn’t migrate mainly through Anatolia, but by crossing the strip of land between the Black Sea and the Caspian Sea, then turning west.
Also, and this is typical, their dating is misleading. The migration may have begun around that time, but it happened in a number of waves, with the largest groups of immigrants not arriving until thousands of years later.
There is actually a lot of DNA evidence that there was also a southern Mediterranean route via Crete, Sicily / Italy to Spain.