The only thing we know for certain is that Saavik and David had enough time to transfer over to the Grissom and arrive at Genesis to begin their scans and studies, but that doesn't require all that much time given that starships can travel at high warp and the request by Saavik and Kirk's son to go back to Genesis aboard the closest available science vessel wouldn't have taken long at all to get the greenlight.
As soon as the Enterprise got her subspace radio online again or Starfleet grew concerned that two ships and a station were no longer responding, there was a ship sent out to investigate.
Or two, one of them being Grissom. The Reliant crew and Carol head onto Earth on one, David and Saavik board Grissom and go back.
Carol's ship arrives, someone talks, "Genesis" rumour starts.