Normally when you receive a Quest Reward, such as Dream Prize, you'd look through the Adventure deck since you always get teleported to the Warlock's Cave on the main board. So that's the deck you use. However, the Chivalric Knight has the potential to get Quest Rewards while in the Dungeon or Highlands.

Now usually the term "Adventure deck" is a catch-all category based on what board you're on. So "Adventure Card" means "Dungeon Card" while in the Dungeon. We've seen this from rulings on the Prophetess for example.

My question is with regards to Dream Prize and the Follower version, should it strictly mean "Adventure deck" even if the Chivalric Knight is on another board? Or should the above ruling continue. Personally I feel it's better for it to always be the Adventure deck, especially if you have all of the expansions, as there's better potential for goodies!

I think that the Rule for Dungeon (or Highland) concerning effects that mention Adventure Cards applies to Quest Rewards too.

Dungeon (or Highland) decks have less valuable Objects than the main board deck, but missing a Turn to help another Character is still a player's choice. Your Reward will always be a random one, so it's a risk you take, especially in the Highlands where you have lots of Trinkets that are not enticing prizes.

Of course an official answer on this matter is welcome.