Wealthy individuals moved into "gentrifying" neighborhoods _after_ massive movements of capital, not before. In 2007, no professional was leaving the upper east side to move to Williamsburg or Prospect / Crown Heights. After Bloomberg rezoned the waterfront and rammed Atlantic Yards through, boatloads of money moved in. Vacant lots and abandoned buildings were torn down, new ones were built, "luxury" housing stock was created and _then_ rich people moved in.
It's not all that different than VC money in startups - investors are sheep. Once it becomes clear a big fish has made an investment in an area, money floods in and drives up prices. To justify the increase in land values, investors have to raise rents. To raise rents, they need to improve the housing stock. This creates the inventory that the wealthy purchase.