I'm often skeptical of these claims. In the SF Bay Area I can understand why this might be the case, since there are a lot more big tech companies shelling out huge salaries, but the Seattle area only really has two big ones: Amazon and Microsoft.

A little back of the napkin math: I'm going to guess that the number of engineers Amazon has in Seattle will be roughly equal to what they were advertising for their second HQ, around 50k. According to Wikipedia the population of the Seattle metro area is about 3.8 million, so the Amazon engineers represent just 1.3% of that - and those engineers haven't come in a huge wave, they've been trickling in over the near 25 years that Amazon has been in business. A major metro area should be able to handle that kind of shock.

There's something more at play than just well-paid tech workers pushing up the housing prices. A combination of low interest rates and restrictive housing rules would have a much bigger impact.