In essence, it’s based on how many people don’t take their seats. Let us say, 100 people, got into NA. Let us also say that 10 people were put on their waitlist. If 5 people decided to go to a school that wasn’t NA, those 5 people’s spots would be given to 5 of the e10 people on the waitlist. How they pick the 5 students out of the 10 is unknown, but they obviously have a system in place. That’s pretty much how the system works in real life, except with more people in the accepted pool and the waitlist pool. The reason it happens in mid-April is that they need to know who’s decided to attend NA, and who’s going somewhere else so they know how many spots they can give to waitlist kids. I wish your child good luck! 
I got accepted into Delbarton, but got waitlisted at NA and Pingry.
Hope this helps. 