The intention of MILD is to set up associations between dream signs and dreaming. It's like telling yourself that the next time you see your Mom you want to remember to tell her that her boss called for her. Or the next time you go to the store you want to remember to stop by the gas station and air-up you tires.

MILD is mainly about recognising dream signs and dream-like qualities and associating them with the notion that you must be dreaming or you wouldn't be experiencing them.

I don't think MILD has any less likelihood of working in the first REM periods than any other method. It's just that you are typically less likely to recall the dreams from your earlier dreams, hence LeBerge's reminders to recall the dreams.