This source suggests that ash was not the killer of most people in Pompeii during the eruption of Vesuvius. Instead, we hear that they must have died of extreme heat. A study conducted found that most people died during the fourth pyroclastic surge, which didn't contain much ash and was relatively slow. However, temperatures during this surge got up to 300ºC, which is more than enough to cause many deaths very quickly. Studies done on bones also point to the fact that they were exposed to a lot of heat, compared to bones of the dead that were not killed by heat. This article also explains the postures of many of the casualties were caused by muscle spasms experienced in extreme heat during a shock, and not because of suffocation by ash. This source is reliable as a lot of research went into it and proves the point that the people who died at Pompeii during the eruption were in fact killed by exposure to extreme heat.
During the eruption of Mount Vesuvius in 79 AD, Pliny the Younger described the eruption in two letters, talking mainly about how his uncle died during it. It describes how what actually killed his uncle was the vapour from the eruption which suffocated him, and he was found with no damage done to his body. This tells us that no debris or lava killed Pliny the Younger's uncle, and that it was really just the smoke and gases that had come out of the volcano instead. This may not be a particularly credible source, as it is written by someone related to a casualty of the Mt Vesuvius eruption, though they weren't there to experience it and haven't done any studies which can prove the actual cause of death.
Dio Cassius, a Roman historian, described how the event of the eruption of Mount Vesuvius at Pompeii unfolded, though he did this 150 years after it happened. He accords with Pliny, saying clouds of smoke and ash killed most people who died during this event. This supports the idea that the main cause of death at Pompeii was suffocation from what pyroclastic flows contained. However, there is no direct evidence or studies linked to this to prove any points that Cassius makes here.
The remains of people who died at Pompeii in the Herculaneum boat shed were found. Archaeologist E. Lazer performed autopsies and found that the respiratory tracts were blocked by mucous and ash, or that they were likely killed by the intense heat created. Evidence for pyroclastic surges caused by the eruption was also found, which contained ash and debris that could have killed many people. The location also shows that many of the people were trying to escape by sea. This source suggests that the cause of death for many people was the sever heat caused by the eruption or the ash and debris in the several surges of pyroclastic flows, proven by autopsies on dead bodies at the site.