I can't help with the prehealth stuff since my school doesn't do it that way (I organize with each professor when they are sent).
Every school I encountered wanted the letters with the secondary, with the exception of Duke which wanted to wait until the interview (which was really awkward IMO, since they also required 4 when the average is 3).
The other exception I guess would be the schools that are doing that AMCAS letter thing where you send the letters to AMCAS and then they get sent to the schools. They still probably want the letters with your secondary, but you don't have to worry about it because you just send it to AMCAS and they take care of it for you.
I'd imagine the prehealth person would know all this and probably knows to wait to send the letters.
I would also stress, like other people here, to ask and get the letters done sooner rather than later. I thought asking in May would give my professors plenty of time, but my last letter didn't get sent until October! So I was a very late applicant just because of one stupid letter, which was quite annoying. I still got interviews and acceptances, but I know I would have gotten more if I had gotten in complete earlier. (Ironically the one letter that took so long was my non-science professor. I should have guessed that a music professor would have trouble with a deadline...)