The landfall ability triggers whenever a land enters the battlefield under your control for any reason. It triggers whenever you play a land, as well as whenever a spell or ability (such as Rampant Growth) causes you to put a land onto the battlefield under your control. It will even trigger when a spell or ability causes another player to put a land onto the battlefield under your control (as can happen with Yavimaya Dryad's ability, for example).

When a land enters the battlefield under your control, each landfall ability of the permanents you control will trigger. You can put them on the stack in any order. The last ability you put on the stack will be the first one that resolves.

Admonition Angel's landfall ability and its last ability are linked. The last ability refers only to cards exiled with its landfall ability.

If Admonition Angel's landfall ability triggers, but the Angel leaves the battlefield before it resolves, its last ability will trigger and resolve first. All previously exiled cards will be returned to the battlefield. Then the landfall ability will resolve and exile the targeted permanent forever.