Angel of Condemnation - Exile creature with second ability
Since it's not specified by the effect, the creature enters the battlefield under its owner's control.
Generally, if the effect that does the zone-changing does not specify it, an object that changes zone has no memory or relation to its previous existence. It doesn't &quot;remember&quot; its previous controller when it returns to the battlefield, so it takes its owner instead.

400.7. An object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence.

In your specific case of an object that is &quot;exiled until some condition is true&quot;, the rule is explicit in the Comprehensive Rules:

610.3. Some one-shot effects cause an object to change zones &quot;until&quot; a specified event occurs. A second one-shot effect is created immediately after the specified event. This second one-shot effect returns the object to its previous zone.
610.3b An object returned to the battlefield this way returns under its owner's control unless otherwise specified.