Clarification about Azurite Channeler in Ascension: Deliverance
The way cards like that work in general is you place the card where the banished card came from. An example of this is Guide of Lost Souls from Dawn of Champions


  You may banish a card in your hand or discard pile. If you do, replace it with a Mystic or Heavy Infantry


When using this card in the iOS app the replacement card goes into your hand if the banished card came from your hand or into your discard if the card came from there. While most other cards specify placing them in your hand I think the replacement text means to put the new card in the same place as the other one came from.

I am unable to find anything in the rules or faq in regard to this but I can confirm this is how the iOS app treats the action.