Ahh, you mean, on a cave map, the background is ALWAYS cave, regardless of where you are?

Go into the map properties, and in the "Battle Background" area, click the "Specify" radio button and the [...] button under it. Now pick the map. Make sure to hit OK!

The other method is best used for world maps.. if you're over a desert, you'll get a desert background, and on a grassland area, you'll get grasslands. The other tilesets default to grasslands on most of the tiles - a quick check shows that all but the lava and water tiles (not the waterfall or whirlpool) in the Dungeon tileset are grassland for some reason - I guess they wanted you to set the background for the entire map manually.