Page 10 has the bulk of the rule that applies here:
“:” means the result of an action or effect or the fulfillment
of a condition. For example, with the Great Lighthouse, each time you buy a Progress Card for 3 Gold, you gain a Book; with Notre Dame during the Production Phase, you gain 3 Books if you have the most Stability
Abilities on cards are always trigger:effect. Where the trigger is itself an action that the card provides, it will always say so on the card in the form of "Action : effect". Otherwise, when the trigger is met, the effect takes place.
In the case of the Ming Dynsaty the trigger is when you take a worker, be it in the growth phase (the main place that you are able to do so), or via some other ability that allows you to do so, such as Hawaii, and Lincoln amongst a small pool of cards that do so. When you do so you get +4 food.