when one draws a dragon tile and places it in a city with his/her builder, then does he/she get to take another tile like usual before the dragon starts moving?
No. The tile is laid and followers can be deployed as usual. The Dragon then moves. After Dragon movement, the player may now take the second builder tile and finish the double-turn.
That's on page 65 of the CAR as well, although it's not very clear. The normal turn is 1. Draw and place a tile, 2. play a follower, 3. score (as shown on page 65). With a double turn, you just repeat 1-2-3 again, although it is still considered to be the same turn. Perhaps Matt should add that to his table.
