Yes, ber5897 has it generally right. Timing doesn't really matter.
Deild really just is waking up and falling asleep consciously in rapid succession, the process should be as groggy as possible to make it easier to fall asleep. Generally REM cycles don't pose much of a problem because if you fail a DEILD and fall asleep nothing bad has happened. Worrying about REM will only make it worse. Just try to wake up and fall asleep consciously as fast as possible, sure you can keep your mind busy but don't don't get in the way with worrying or over thinking.
Deild may seem like it is a very intense experience but it is not different than WILD, I often barely remember my attempts since I usually try be as sleepy as possible so that falling asleep consciously is really easy.