The video linked in the article claims they can harvest a tree every 9 years.
A tree reaches maturity after ~25 years after planting, and the first harvest is usually low quality, so it doesn't bring money. After the first harvest it can be harvested every 9-10 years, and you can do so for hundred of years (a healthy cork oak can live for 5-600 years).
Cork does grow on trees, but slowly :).
"It takes at least 20 years for a tree to mature so it can be harvested"
If cork demand doubles tomorrow it means you will have to plant new trees and it will take at least 20 years before those trees are mature enough to be harvested.