Normally, all communication between the beneficiary and NVC (and/or the Moscow embassy) is electronic other than sending the beneficiary's passport with visa and accompanying documentation (sealed envelope, etc.) back after the interview. Ignore the text about the NVC contacting you in the CEAC status pop-up; it doesn't apply to K-1s.
Anastasia never got any print mail from the NVC or Moscow (and most consulates are the same). She did get an email from the embassy just before the calendar opened for her, but I'm not entire sure if that was a reply to her previous emails or standard (it had been a couple weeks since NVC ready at that point, though the first week or so was during Russian holidays).
George & Darya reacted to DaveAndAnastasia in NVC --> Moscow --> Letter... What is the timing?