Hypergenesis vs Containment Priest - How does it resolve?
Containment Priest exiles just Progenitus. Admonition Angel's landfall ability triggers once.

Containment Priest's ability is a replacement effect (rule 614.1a says "Effects that use the word 'instead' are replacement effects."). Rule 614.4 says


  Replacement effects must exist before the appropriate event occurs—they can’t “go back in time” and change something that’s already happened. Spells or abilities that generate these effects are often cast or activated in response to whatever would produce the event and thus resolve before that event would occur.


Admonition Angel enters the battlefield before Containment Priest, so it is not exiled. But by the time Progenitus would enter, Containment Priest is already on the battlefield, so Progenitus is exiled instead.



Admonition Angel's Landfall ability (like any Landfall ability) is a triggered ability because rule 603.1 says


  Triggered abilities have a trigger condition and an effect. They are written as “[Trigger condition], [effect],” and begin with the word “when,” “whenever,” or “at.” They can also be expressed as “[When/Whenever/At] [trigger event], [effect].”


Rule 603.6d says


  Normally, objects that exist immediately after an event are checked to see if the event matched any trigger conditions. Continuous effects that exist at that time are used to determine what the trigger conditions are and what the objects involved in the event look like. However, some triggered abilities must be treated specially. [Several exceptions that don't apply here].


Like with Containment Priest, immediately after the Mountain enters the battlefield, the Admonition Angel is already on the battlefield, so its ability triggers.