2021-03-19 : Containment Priest's last ability won't affect any creatures that were cast, including ones cast from unusual zones such as your graveyard.

2021-03-19 : If Containment Priest enters the battlefield at the same time as other creatures, its ability won't affect those creatures.

2021-03-19 : If Containment Priest enters the battlefield without being cast, its ability won't exile itself.

2021-03-19 : If a noncreature card wasn't cast and is entering the battlefield as a creature (due to an effect such as that of March of the Machines), it will be exiled. Conversely, if a creature card wasn't cast and is entering the battlefield as a noncreature permanent (for example, Heliod, Sun-Crowned with insufficient devotion), it won't be exiled.