("Each player may Push a Beasts" would not be sufficient - cases like that don't represent Spirits doing things, the game just needs a player to make a decision for a Fear or Event card. It would have to use the word "Spirit".)
Usually, the wording "when you (do X)" is used for your pieces or other game components: e.g., "when you Forget a Power Card" or "when you uncover this spot on your Presence track" or "when your Presence is destroyed". Those can obviously happen as a result of many different sorts of actions, not only your own. Tags: Actions, Beasts, Fly Fast As Thought (Many Minds Move as One), Many Minds Move as One, 0 more...