There was a situation that came up at Maryland States this past weekend, and neither myself nor the Head Judge could find an answer among
Ashcloud Phoenix's Gatherer rulings nor the Comp. Rules. The situation was:
A player activates
Ashiok, Nightmare Weaver's +2, exiling three cards from his opponent's library. One of those cards was an Ashcloud Phoenix. He then asks a judge the following: if he puts the Phoenix onto the field with Ashiok's -X, and it then dies face-up, would it return to the field under its owner's control, or under his control? The ability doesn't specify under whose control the Phoenix returns to the field.
We agreed upon the Phoenix returning under the Ashiok player's control, rather than its owner's. This is different than the reminder text provided for
Banisher Priest and
Banishing Light, but we felt that the fact that Ashcloud Phoenix instructs the controller of the trigger to return it to the field indicates that it should return under the control of whomever controls its “when ~ dies” trigger.