Containment Priest cares about objects as they would exist on the battlefield, so it should not exile an Old-Growth Troll returning to the battlefield due to its own ability.
One of the rulings on Containment Priest confirms this is incorrect behavior.
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.(2021-03-19)