"Just thinking of the reverse turn foxtrot, surely the man would start his rotation before the right foot passes the (standing) left"
Yes, of course.
The issue is one of definition however - there are many different places we can measure, and in the formal technique each applies specifically to some things and not to others.
- Body turn or rotation, known as CBM when it's in the direction of the moving foot, simply means that the body rotates in the room.
- Change of the alignment of the moving foot is what is literally meant when the technique books use "turn" without explicitly specifying something other than the feet. Turning the moving foot does not necessarily mean that the body has rotated, and it does not necessarily mean that the direction of movement has changed.
- Direction of movement in the room. This does not necessarily change either when the body rotates or when the feet turn, though both of those often set up an eventual change in direction of movement.
There are a lot of varieties for how the different pieces intereact, but the most common one is a process drawn out over two to two and a half steps of dancing. In its simplest form this consists of:
first, rotate the body (CBM)
next turn the feet
finally, establish a new direction of
movement in the room.
But there are some variations - for example, in the weave from promenade after a whisk the man will not need to turn his body, but he does need to turn his foot already when he places the first step. The actual change in direction of travel in the room does not occur until later in the figure.