It isn't clearly enough stated in the CAR, but you can only do it once.
So, double-turn is a single turn which includes, but is not exhausted by, identical two parts. Those parts consist of the usual stages of placing a tile, deploying a follower, and scoring a feature. Any game effects which relate to those stages of the game can be repeated. Dragon movement, for example, is triggered by placement of a dragon-tile; and so it occurs twice in a double turn. The same goes for moving followers to Carcassonne; that's triggered by placing a tile which completes a feature but not scoring any points in the process—hence, it happens twice in a double turn.
Then there are events which occur outside those steps—usually at the start of the turn, or at the end. Bonus points from the fairy, for example, occur at the start, before a tile is even drawn; and escape from a besieged city occurs at the end, after everything else has been completed. Ransoming prisoners is another example here. These things only happen once in a double-turn.
The problem is that this is a recent—and inconsistently employed—development in the rules. At the time when Aldaron was writing his summary (and I was helping him), a double-turn was considered to be two separate turns, and as such the 'beginning' and 'end' events happened twice in a double-turn. HiG have since then revised this, but even then there are problems.
For example, I've just noticed a contradiction between the Count, King and Consorts rules, which make this distinction clear, the answer to Q2 of the
Latest from HiG:
The builder-turn is not an extra turn, but a part of the regular turn (the double-turn). Both parts of the double-turn are identical, although the fairy (3rd expansion), for example, only gives bonus points at the start of the player’s turn, and a figure can also only be moved to Carcassonne (Count) once.I need to check this one before we go any further. The way I've described it above is the way it should work, though.