The fact it's been travelling so long, that's warp field has collected a layer of material so emmense like a dust cloud building over it, would take many many years of constant warp travel through interstellar mediums to gather it all.
The cloud wasn't dust. It was Vejur's power field reacting with interstellar matter at high warp. When Vejur slows down the cloud goes away. "Luminescent power field" is how the Epsilon 9 station describes it. Roddenberry goes into greater detail in the novel.
Oh, and to answer the thread: Hell yes. Both of them are at best accidentally genocidal. Neither stops because they are convinced of the worth of the lives they are threatening (unlike One of Our Planets is Missing). Both stop because they get what they want, damn the consequences.
Vejur knows only that it needs. So did Soran. So did Apollo.
"Only human arrogance would assume the message must be meant for man." And only Whale Probe arrogance would assume the message is worth wiping out most of the surface dwelling life on the planet (at least)!