You're correct that it's usually said that there were either two or three survivors of the Mount Pelée eruption. By this it's meant that only two people who were living in the town of St Pierre, which lay at the foot of the mountain and directly in the path of the nuée ardente, or pyroclastic flow of superheated gases ejected by the eruption, survived the eruption. The name of Havivra Da Ifril is sometimes added to this total, but her circumstances were rather different, as we will see.

The figure of two or three survivors is in any case a somewhat misleading one. The eruption did kill the other 30,000 or so people who were actually in the town at the time, which made it by some distance the most catastrophic volcanic event of the last century. But there were some additional survivors who were on the fringes of the pyroclastic flow, or who were on ships in the town's harbour – and of course many who lived elsewhere on the island of Martinique and were not directly affected by the nuée ardente.

Alwyn Scarth, a geologist who wrote the most complete recent study of the eruption, suggests that "a survivor of the nuée ardente should be defined as someone who lived after being touched, burned or buffeted by the eruption," and on that basis many more than three people escaped. Scarth says there were at least 64 of them, and perhaps as many as 111 – 13 of whom were on land and in the path of the eruption and further 20 of whom survived on the ship Roraïma, in St Pierre harbour (it's not clear how many of those on the ship lived for more than a few days, but some of those 20 certainly died in the aftermath of the eruption). He names, for instance, a man named Simon Taudilas, who was on the extreme edges of the nuée and "thrown down by the blast," but was otherwise unscathed.

So the "two survivors" or "three survivors" of popular accounts were simply those identified in the aftermath of the eruption as having had especially miraculous escapes. Scarth concludes that

a kind of semantic slip has led many to assert that only two people survived the whole nuée. It also made for a more dramatic story, which added to the human interest of the eruption... [The survivors] lived through the onslaught of the nuée ardente because they happened to be where its effects were attenuated at the critical moment. On land, they were on its outermost edges. On board ship, some people survived in well sealed rooms; others were protected by the bodies of comrades who fell on top of them; and one or two lived because they managed to stay under water until *the *nuée passed over.

The three people most frequently named as "survivors" of Mount Pelée were:

Louis-Auguste (or Ludger) Sylbaris, commonly referred to as Louise-Auguste Cyparis or Ciparis, who had been locked up in the St Pierre jail (which was formerly a French colonial barracks) and was serving a sentence of eight days in solitary confinement for slightly wounding a man with a cutlass while drunk and disorderly. Sylbaris was then about 25 and very powerfully built – he was known locally as "Samson". He was confined in a one man cell that had formerly been a magazine, built with extremely thick walls. The cell was also located in a protected hollow behind the prison walls, and was cut back into the mountain itself. The only openings in the cell were two gratings, one of which was in the door. Although the prison was in the path of the pyroclastic flow, and Sylbaris was badly burned, he did not inhale the gases and so survived and was rescued three days later.

Sylbaris later toured with the Barnum & Bailey circus, where he was exhibited in a mock up of his cell, and he lived a further 27 years, dying in 1929. He was the subject of numerous newspaper articles and is featured in all of the books written about the disaster, perhaps most notably, at least from a literary point of view, in Patrick Leigh Fermor's sole novel, The Violins of St Jacques.

Léon Compère-Léandre, a shoemaker, claimed to have survived inside his own home, about which essentially nothing seems to be known, but which was apparently closer to the edges of the pyroclastic flow than the prison that Sylbaris had been locked up in. His account of his survival – which, incidentally, suggests that others, never named, may possibly have survived in the same location – was that

I felt a terrible wind blowing, the earth began to tremble, and the sky suddenly became dark. I turned to go into the house, with great difficulty climbed the three or four steps that separated me from my room, and felt my arms and legs burning, also my body. I dropped upon a table. At this moment four others sought refuge in my room, crying and writhing with pain, although their garments showed no sign of having been touched by flame. At the end of 10 minutes one of these, the young Delavaud girl, aged about 10 years, fell dead; the others left. I got up and went to another room, where I found the father Delavaud, still clothed and lying on the bed, dead. He was purple and inflated, but the clothing was intact. Crazed and almost overcome, I threw myself on a bed, inert and awaiting death. My senses returned to me in perhaps an hour, when I beheld the roof burning. With sufficient strength left, my legs bleeding and covered with burns, I ran to Fonds-Saint-Denis, six kilometres from St. Pierre.

This account has been treated somewhat sceptically, and it has been suggested that – because there is little reason to suppose Compère-Léandre's home was especially well protected from the nuée – he must have escaped in some other way, perhaps by jumping into the sea. If so, it is unclear why he chose to spin such an elaborate tale at such a variance from the facts.

The difficulty of knowing what became of Compère-Léandre is compounded by the fact that, while he lived on in Martinique until his death in 1936, he never sought to profit from the experience and so was much less written about.

Havivra Da Ifril is not mentioned at all in many accounts of the Mount Pelée disaster, and it is far from clear whether the story she told of her survival is true. She claimed to have been on the mountainside, running an errand for her mother, when she saw a "boiling red river" – presumably lava – approaching her. She ran to the seashore, and jumped into a small boat, which she rowed out to sea. She was burned by falling stones and ash, but was rescued later by a French warship.

If this account is true then it seems that Da Ifril was some way away from the pyroclastic flow which killed the vast majority of those caught in the eruption, and she would appear not to meet Scarth's proposed definition of a "survivor" of the eruption.

In any case, the simple answer to your question is that none of the survivors of the eruption wrote their own histories of it, though all three of those most commonly named gave verbal accounts of their survival, and, in Sylbaris's case, he must have discussed the events of 1902 hundreds, if not thousands, of times over the years. Scarth gives the most detailed account of possible survivors that I have seen, but he doesn't name all 64+ people he discusses, and it would seem that since quite a few of those people were part of small to moderately sized groups, which were written about collectively, in at least some cases no names were ever actually published at all. An additional difficulty is that no formal tracking of survivors was ever done; Scarth believes a significant proportion of those who were originally reported to have survived would have died later, and while his 64+ figure comprises those he is convinced survived at least the first few days or weeks, it could well be that at least some of those died later specifically from the after-effects of their experiences.

To gather more would mean going back to contemporary French records and newspaper accounts.

Source

Alwyn Scarth, La Catastrophe: The Eruption of Mount Pelée, the Worst Volcanic Disaster of the 20th Century (2002)

John Withington, Disaster!: A History of Earthquakes, Floods, Plagues, and Other Catastrophes (2010)