Maybe your town PD has different rules, but in my case it was by mail, not by phone. In fact, I was the one who wrote addresses on the PD envelopes on my appointment when I brought in the papers. I contatced my references to make sure they folow-up, and they did.
As for the fingerprinting, it is all "automatic", no need to follow-up on this.
The whole process, from application to getting the papers took about three months. As I can see from the papers, the FID was ready in one month, but permits apparently took much longer. I guess the officer in charge didn't want to make extra appointment just to give me FID and another one for permits. No problem with that.