To trigger these, you need to deploy a set during the first hand of a new tournament, preferably when it is your turn.
The first time you do it, you are introduced to the House Rule that explains why The Inventory changes, but the second time, you get setting specific introductions.
So far, my favorite is the Aperture room's intro, especially since GlaDOS points out that the player has no idea what they've done now that she has access to bring turrets and portals into play.
Second would have to go to the Boarderlands room, but only because of Brock's line of how it looks like "a strip club with explosives.":D