The emails come almost instantly. If you don't have them, then you probably won't get them. Once you call and get the full numbers from a CM, you can look up the ADRs online and resend the email to yourself so that you have a written record of the ADRs from Disney.
edit: I just checked my own email for the ADR I booked this morning and there is no email there yet. Maybe the system glitch is causing emails not to be sent at all or maybe there are delayed this morning?