It's supply and demand economics: if there is a low supply of workers and a high demand for them, then employers are supposed to compete for them with more pay, more benefits, training/education, etc. When the supply of workers is artificially increased, then companies have less incentive to compete. It becomes a buyer's market for employers.
General equilibrium exists though, if the supply of workers increases you usually see businesses which were previously non-viable appear to take advantage of them at similar rates.
You can illustrate this by doing the other direction: if we killed half of the workforce, would real wages double. Unlikely! You'd probably just see broad-based inflation for a while until wages equalized again.
It can't be due to fundamental skill, though! That same engineer's earnings statistically triple upon moving to the US, which is why we should allow more of them in: people are more productive in the US, and we all benefit from their productivity (most obviously fiscally, but less obviously through products that wouldn't exist in the counterfactual).
