Based on my own cursory observations of the population flux in the Bay Area, I believe your analysis and thus conclusion is based on a false premise.
That analysis assumes that the hiring base is predominately drawn from local people. Speaking anecdotally, I know many people who graduated from college and headed to the Bay Area to look for a job. I myself moved to Mountain View for a job, then later moved away.
A more complete analysis along the lines you took would look at where people in engineering and product management were, say, 1 or 5 years previous. That are would likely better characterize the relevant population statistics.
As an obviously contrived example, suppose people in engineering and product management are only in the Bay Area for 4 years, burn out, and leave, and suppose the companies offer free relocation from anywhere in the US. Then it doesn't make sense to look at the local demographics.
As a more real-world case, consider a place like Los Alamos National Labs, which has a large number of people from around the world working there, with a relatively high turnover rate partially due to interns, post-docs, and visiting professors. Los Alamos county was carved out for the lab, so the demographics of the county reflect the lab, but most of the people working at the lab are not from Los Alamos.
I do not have access to these sorts of numbers, merely pointing out how it's not easy to interpret the numbers you gave, or the certainty of your conclusion that it's a "not unexpected" result. I suspect the uncertainty is actually very high, and a shot-in-the-dark/back-of-the-envelope estimate isn't likely to be useful.