Rest and Perish Song works the same way as before.
Originally Posted by Fat DDRMaster
I think someone also tested to see if Rest and Perish Song have an extra turn for their effect and proved that they didn't. I don't know where the post was, though.
I tested Rest twice, and my Pokemon woke up after 2 turns of being unable to move (due to sleep).
Also, I would like to add that when I used Rest, the opponent used Torment. The next turn, I could not choose Rest, due to Torment. I know Torment was changed to work like this, but I thought it's worth mentioning.
The turn you use Perish Song, the count is 3. At the end of the next turn, the count is 2. You die at the end of the turn when the count is 0.