I think that a lot of places would want to mail them to you, because they want to be able to look up and copy the records when they get around to it, not right then and there with you waiting. Some places even have outside contractors who come in on a schedule and copy records to be sent out. So in that sense, you are lucky that you got service on the spot. But any doctor's office should be able to tell you whether they can copy the records while you wait or if they only do it later and then mail them out. If they only want to mail your records to you, I think I might give them a self-addressed, stamped envelope with my name on it and the address of a trusted friend who would keep the mail, unopened, until I could pick it up. You might also look into getting a PO box for privacy. I have the smallest size PO box, and it costs, if I remember correctly, around $100 a year.
No, they don't typically mail your records and also give you copies on the spot. I'm surprised you got them so fast, honestly. If you are over 18, and DONT have a form filled out stating they can contact your parents regarding any issue, your fine. I would look into it. Many also don't know, that when you say...switch doctors, or a specialist is asking for records and you may not want them all to be shared, you have the right to request exactly what you want sent to where. You just have to spell it out. For example: "please send all records to Dr so and so at such and such address, NOT INCLUDING any tests performed in office or sent to another facility for testing" this may raise some eyebrows, so usually "Please send a copy of ADHD evaluation, only" or "please send xrays done in years 2007-2009 for my left arm only please" works just as fine.