Are rooms drawn because of tiles and cards always considered 'discovered' and thus the symbol on the card executed?
Any time you enter a newly-drawn room, you must resolve the symbol in that room if it has one.

The only way a room can appear in the house without having you enter that room at the same time is during a Haunt's setup instructions. During these setup instructions, you will ignore any symbols in the rooms, because there is no player entering the room to resolve the symbol.

The events that can cause you to need to draw a new room tile will also tell you to move into that room, and when you do so, you must resolve the symbol. Note that if you ever ignored symbols in this way, you could end up with a game where the Haunt never begins (you ignore an Omen symbol, and then you only have 12 Omens instead of 13 to resolve. And it is possible, though very unlikely, that you will still pass the Haunt role with 12 Omens. But with 13 Omens, it is impossible to pass the role so the Haunt begins).

The closest the rules get to being clear about this is here:


  A room may have a card symbol on it. The
  first time you discover a room with a card symbol, you must
  end your move in that room and draw the appropriate card.


It doesn't specifically define "discovering", but it seems that the only assumption where the game makes sense is that discovering is any form of drawing a new tile and entering that room.

Note that in the first edition, the event Revolving Wall specifically tells you to ignore any symbols in the new room, but this is a mistake due to the never-ending game problem and was fixed in the second edition. See the errata for the game:


  Revolving Wall -- This states, "Icons in [the newly drawn] room do not affect you this turn." Does this mean the icons affect you (thus ending your movement) on the next turn?
  
  
    Errata: Any icon in the new room does affect you when you enter. Otherwise it is possible (though unlikely) to have a game with no Haunt.