It had to do with the pyroclastic surge & flow and generally the direction in which the force of the flow was ultimately directed by the atmosphere and geography of the mountain itself.

My primary source is below and is a great compilation of academic articles on various topics regarding research of Pompeii and Herculaneum. It includes an article on the mechanics of a subduction volcano and how this eruption profile buried Pompeii in particular. Some of this is also drawn on earth science study I performed as an undergrad.

Regarding georgraphy of the area - Pompeii is due east/south east of the crater. Herculaneum is much closer to the crater but due west. Naples is about equal disantce from the crater as Pompeii but North West/West. So, at a basic level Naples was clear in the opposite direction as Pompeii and Herculaneum was much closer to the crater than Naples.

The gist is that the volcano is formed via the subduction of 1 teutonic plate under another - often this occurs between sea floor and continental shelf as the sea floor is a denser material that will tend to naturally sink underneath the continental shelf back towards the Earth's core, melting it and in some cases causing a hot pocket to be trapped somewhere underneath the continental shelf. This hot pocket will continue to capture molten material and gas until it builds enough pressure to release this material through the upper layers of the shelf. This process will occurr repeatadly over time which causes the mountain (effectively the mountain is remaining sediment from past eruptions). As there had been prior eruptions, there was also an existing rim along primarily the north and eastern portions of the mountain, which seems to have played a roll in containing some of the eruption towards the south and west.

Now, during the eruption the initial tremendous force of the gas escaping propels what is effectively a column of hot gasses, debris and molten material up into the air and into our atmosphere. This initial phase of the eruption is known as the Plinian column- you guessed it - because our buddy Pliny the Younger described this event during the eruption of 79AD. This lasted for roughly 12 hours before the initial pyroclastic surges / flows which I noted above began to play a role. During this time this column of debris was anywhere from 14-30km into the atmosphere and the wind carried this plume south (towards Pompeii). As such, Naples and more surprisingly Herculeaneum which was more or less at the base of the mountain did not see heavy fallout of material from this column.

Pompeii did, and as such pummice and other rocks (predominantly pebble sized but some ranging up to ~a fist size) would have been falling on the city for ~12 hours. This material built up and began burying buildings, caving in roofs.

After about 12 hours the first of 6 pyroclastic events occurred. This is caused by the column beginning to collapse in on itself and forcing much of the built up gas / debris out around the crater. This begins with a surge of fast moving and hot gasses followed by a slower moving wave of debris. Generally the surge will be contained to a smaller radius around the crater prior to the gases dissapating or otherwise losing momentum, while the flow of material will be propeled on the ground by momentum a larger distance.

Over the next 12 hours these 6 surges and flows began working their way out around the crater. The initial 2 surges effectively took out the populace of Herculaneum given it's proximity to the crater. These began damaging buildings there (though some materials were actually preserved by exposure to the hot gasses). The flows then followed but in these early cases the crater to the North/East of the mountain helped to contain them and these early flows did not yet have the momentum to reach down to Pompeii (though they did run over Herculaneum).

The next 4 cycles of this process were larger and eventually the final flows did begin to breach the walls of Pompeii as well as overcome the north/north east rim of the crater. However, given the geography of the mountain, again, the fall out extended much further southeast than northwest - though in the maps I've seen it does appear these flows did in fact reach towards Naples, they just didn't reach the city itself. Pompeii on the other hand had now been buried by about 18 hours of pummice falling out of the Plinian column so the flows once they reached the city destroyed much of what was remaining above the debris.

So to summarize - Pompeii had the fall out of debris from the column off and on for the entire 24 hours of the event given wind influence on the column. Pompeii then due to the geography of the crater was also eventually it by the final and largest pyroclastic flows. Herculaneum did not get fall out from the column, but being right next to the mountain saw the full brunt of effectively all of the pyroclastic events (surging avalanches of hot gas and debris when the column collapses). Naples on the other hand was protected from the column due to the wind, and ultimately the rim around the crater offered more protection against the pyroclastic events in the direction of Naples. However it's worth noting that if Naples was as close to Vesuvius as Herculaneum is, it would have been hit by the later flows. So it is the combination of distance and geography of the crater than ultimately saved it.

Naples is still a considerable risk of damage due to it's proximity to Vesuvius and the fact that the urban sprawl from the city is now much larger than it was back in 79AD. Luckily subsequent eruptions in more recent memory have tended to be less violent than the eruption of 79AD so they've been more localized in their impact.

If you still have questions I'd honestly suggest posting to a science based sub. Or researching subduction volcanoes. The crux of your question is rooted in our scientific knowledge of this type of volcano as much as our historical record of the specific event. Mt. St. Helens and events in Chile and Mexico over the past 100 years have given us more knowledge on the process of a subduction volcano's eruption, and investigation of the layers of material burying Pompeii/Herculaneum have allowed scientists to use that knowledge and re-create the events from this eruption.

Edit:

Source: Sigurdsson, Haraldur. 2007. "The Environmental and Geomorphological Context of the Volcano." Pp. 43-62 in The World of Pompeii, edited by John J. Dobbins, and Peter W. Foss. New York: Routledge.

Also cleaned up some typos from my phone.

Edit 2: Basically re-wrote much of this response after re-reading the article to provde a better answer. Original reply was largely based on 10 year old memory from that reading so I'm hoping this is a much more accurate representation of the science and events that unfolded to answer the question.