...Ah, I withdraw one of my claims. The beam wasn't necessarily visible from one of Vulcan's major cities. All we know is that it was visible from the residence of Amanda née Grayson, which may have been located far away from major cities and possibly far away from all Vulcan habitation, which may be almost exclusively city-dwelling on the infertile world. Combined with a bit of jamming and a merciless elimination of witnesses, this might be enough to hide the true nature of the threat from Vulcan leadership.
OTOH, we witness Amanda walking out onto the balcony and taking a look at the beam well after Chekov informs the shipboard heroes that seismic activity was reported, and even longer after the fleet was launched (supposedly but not necessarily based on that report of seismic activity). It would be more or less inconceivable for Amanda to have arrived in her residence from elsewhere on the planet and be taken by surprise by the local scenery, since transporters on the planet are down. I guess it's a bit more likely that she just woke up from a nap, but not by much.
So it appears that the drilling only started long after the seismic activity did. That's in favor of the theory that the tremors come from black hole travel, not from drilling.
Unless the report on seismic activity arrived after the fleet left Earth, of course. Perhaps the drilling started something like five minutes before Amanda saw the beam; the Enterprise received the distress call mentioning seismic activity while en route; Chekov informed the crew of this new development; and the camera then cut to Amanda walking to the balcony, mere seconds after Chekov had finished his PA.
The initial report of trouble, the one that caused the fleet to be launched, may have been on account of Nero entering orbit with his jammers on and destroying Vulcan local defenses and starships. That'd remove the need to think that the spatial black holes cause the tremors... Also, the idea of the fleet receiving the report while en route frees up the timeline.
Or then certain scenes were shown out of chronological order. In any case, the timeline's an unholy mess, and requires major rationalization. Hardly a case of "everybody getting it just fine"!
Timo Saloniemi