Ten Towers

While you control only House Greyjoy characters and locations, you may play the top card of one opponent's discard pile as though it were in your hand (Limit once per round).

Magister Illyrio

You may play attachments from opponents' discard piles as if they were in your hand.

Correct me if I am wrong, please.

But, since both of these are saying that you can play opponents cards "as if they were in your hand", it means that I have to apply out-of-houst cost.

And that cost can be reduced from either a Neutral House, locations and for example House Bannerman . (Marshalling: Kneel House Bannerman to ignore all gold penalties on the next card you play this phase.)

Unless my opponent is using in-house characters for me aswell, of course.

Yes, OOH penalty still apply to this and you are also correct that normal reducers still work as you are still considered to be "playing" the card.