Before writing the actual answer, it is important to point out that the assault mentioned in the book's title is the shooting of a Dutch policeman who collaborated with the Nazis during World War II. The shooting is perpetrated by the Dutch resistance and takes place in the winter of 1945, a period that the Dutch also remember because of the famine.
In his letter to Tacitus, Pliny the Younger tells the story of how his uncle Pliny the Elder died, namely during the famous eruption of Mount Vesuvius in 79, which destroyed Pompeii, Herculaneum and Stabiae. He died while trying to rescue relatives who lived closer to the volcano.
Pliny the Younger reports in his letter that on 24 August, "a cloud of unusual size and shape had made its appearance" over Mount Vesuvius, and this cloud caused the darkness mentioned in the quote that prefaces the novel De aanslag. There are at least three passages in the novel that mention smoke clouds:
The first passages can be found at the start of the "Second episode - 1952":
De aswolk uit de vulkaan stijgt naar de stratosfeer, draait om de aarde en regent nog jaren later op alle continenten neer.
The ash cloud from the volcano rises to the stratosphere, revolves around Earth and years later still descends on all continents.
The reference to other continents looks strange, until Anton, the book's main character, meets his former neighbour Karin again in the book's penultimate chapter and learns that Karin and her father had emigrated to New Zealand soon after the end of World War II, where her father committed suicide in 1948.
However, after reading the the book's "First episode - 1945", the ash cloud is also linked with the burning of the house where Anton lived as a child. Since the Nazis found the collaborator's dead body in front of Anton's house, they burn it down without asking questions about what happened. We later learn that Anton is the family's only survivor.
Another "eruption" takes place near the end of the "Third episode - 1956", when Anton meets the son of the victim of "the assault". There is a problem with the stove in Anton's room; eventually, the lid flies off and a cloud of soot rises from the stove and covers everything in the room.
Finally, there is another "eruption" during Anton's second and last meeting with the only surviving perpetrator of "the assault" (near the end of the "Fourth episode - 1966"). This time it is an ashtray that begins to produce an extraordinary amount of smoke.
Both of these two "eruptions" take place when Anton or the character that Anton is talking to learns important new facts related to the assault itself or the question of guilt or blame related to that assault.