Containment Priest's last ability won't affect any creatures that were cast, including ones cast from unusual zones such as your graveyard.
Containment Priest's last ability doesn't stop creature tokens from entering the battlefield. It also doesn't affect creatures that were already on the battlefield.
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. Similarly, if a creature card wasn't cast and is entering the battlefield as a noncreature permanent (for example, Heliod, God of the Sun with insufficient devotion), it won't be exiled.
If Containment Priest enters the battlefield without being cast, its ability won't exile itself.
If Containment Priest enters the battlefield at the same time as other creatures, its ability won't affect those creatures.
Standard: Ej legal
Pioneer: Ej legal
Modern: Ej legal
EDH / Commander: Restricted
Pauper: Ej legal
Brawl: Ej legal
Premodern: Ej legal
93/94: Ej legal