As a side note, our coach said that she and her partner almost never do latin lessons with their coaches individually, i.e. partnership is much more critical in standard than in latin.
How to lead the difference between the Chassé Reverse Turn and to do a Heel Turn in Double Reverse Spin. The difference in footwork is that on a Reverse Turn, the swing step, step 2, should be in a line with Man's driving step, step 1. In other words, if Man starts the reverse turn DC, his second step should continue DC in a line from his first step. When leading the lady to do a Heel Turn, Man steps forward and diagonally across with his right foot, cutting off his lady's ability to step forward. Man steps around her.
The instructor talked about a "Standard dance principle": Do not turn the body (hips) until the end of a step. Otherwise, it would feel like Man is leading the lady into a Heel Turn when he is trying to lead the Chassé Reverse Turn.
Zig-Zag is where the lead is especially important, since there is no rise as an additional clue to the lady. Man needs to make sure to maintain balance forward on the second step of the Zig-Zag. Some ladies change weight on their heel turn too early so Man's balance would not affect them, but with other ladies, having Man's weight on his back foot would cause the lady to step forward on her second step, instead of just changing weight to her right foot. Man also needs to keep his body turned to right side leading on that second step, or he will not be able to lead the lady outside partner on the third step.
Closed Impetus. Once again, the first step: Man needs to step straight backwards, not off to the side. Left toe can be slightly turned on the Heel Turn. Feet should not turn out, which makes the dancing look bow-legged.
On the Reverse Pivot and the Double Reverse Spin, here comes the next "standard dance principle", according to our coach: The man leads reverse turns with his head. In other words, Man keeps his head left and back, leading the turn, body follows the head, to keep his balance. The other point of technique, for the Double Reverse Spin, is that on the second step, Man should turn on the ball of his right foot with the heel almost to the ground, and provide rise by stretching his right side.
Clarification point on Rumba Fan: in almost all the cases, the lady is lead to walk straight through step 5 of the fan, while the book has the lady turning to face the man on step 4. The difference is in part a reflection in the change in technique over the past 50 years. Our instructor says what was taught in classes and lessons is used in open figures. For closed figures, the books alignments are still used, as it is not possible for the man to get sufficiently out of the lady's way in closed position.