All such actions in that land are skipped, even if you'd rather let them happen. This includes any normal actions that come from the Invader cards, and also any extra actions that come from effects like the power "Manifest Incarnation" or the event "New Cash Crops Take Hold." (See the B&C rulebook, p. 15, for the distinction between "normal" and "extra" actions.)
This doesn't skip anything the Invaders do due to an Adversary effect, Scenario effect, or Event card unless explicitly the words "Ravage," "Build," or "Explore." For example, when up against Habsburg Mining Expedition, while "A Year of Perfect Stillness" skips the Build half of "Mining Boom (II)," it does not skip the Upgrade.
(Discussion elsewhere) Tags: Skipping Actions, A Year of Perfect Stillness (Vital Strength of the Earth), Paralyzing Fright, Indomitable Claim, 5 more...