[Graham]

The first thing to bear in mind is that all basic moves such as the first move have been developed to help you learn basic building blocks which can be used to develop more complex dance movements later on, and also to get you and your partner used to the basic elements of lead/follow. One important reason for not rotating on count 2 is that you have two counts to reach the twisted out position. If you start rotating earlier the likelihood is that you will reach your end position half-way through count 3, rather than at the end of count 3. Another reason is that it's possible you were planning some move other than a simple first move, which might not work if the lady is rotated during count 2.

If lots of ladies are rotating in freestyle it's possible that your teacher isn't making the move clear enough (or is possibly even teaching the rotation), but it's likely that your lead is allowing them too much freedom. Make sure the lead with your left hand pulls her straight forward, keep your left hand well to your left as you BOTH step in, and try catching her left hip as you're both moving, before she has a chance to rotate. Don't worry if it doesn't always work - if the woman is determined you won't be able to easily stop her. The key thing is making sure your lead is early enough (before she does her own thing).

Both exit options are equally valid. In freestyle choose whichever you prefer, or vary them depending on your mood/the music.

EDIT: As David has pointed out, when the move is really flowing and natural, the distinct positions start getting rounded off, so in fact you will start the rotation during count 2. If this is working for you, there's no need to change, although during the rather more mechanical walk-through in the class it's a good idea to try and stick to the movements the teacher is doing to avoid confusing your partner.