The key part of fire behavior to understand here is how exactly a fire goes about consuming oxygen and exhausting heat and smoke in an enclosed space.

Fire will always need to pull oxygen in, and push heat and smoke out. Oxygen and the cooler air it makes up will always be pulled in on a lower plane than the heat and smoke it pushes out, which as many people know rises. The way this affects the space you’re in and therefore where you want to be (Besides you know, out) is dependent on how many openings to the outside space there are and where they’re located.

If there are two or more openings to the outside space at different elevations, the fire will pull the cool oxygenated air in the lower opening, and push the heat and smoke out the upper opening. This is known as the chimney affect, and as you may have guessed from the name is how fireplaces work. This is why you can have a fire inside your home without dying from smoke inhalation, all the smoke and a lot of the heat is going straight up and out of the chimney, as the fire pulls oxygen in from your living room. This creates a negative pressure in your living space that prevents the smoke from emptying into it, and you just keep the horizontal radiant heat.

If there is just one opening, the fire will have to share that opening between those two functions. The lower half of that opening will be pulling cool air in, and the upper half will be pushing heat and smoke out. If you saw this in person you can actually see the exact line between these two things happening which is called the neutral plane, and you want to stay below it at all times.

There is however a danger here, which is that a single opening like this, often a set of basement stairs in a house fire where the fire is in the basement, allows access down to where the fire is by firefighters, provided they stay below that neutral plane, but only as long as that remains the only opening. Firefighters can and have died fighting their way down basement stairs meanwhile a small basement window below grade is broken either by the pressure generated by the fire or even a fellow firefighter breaking it for ventilation without due regard for the firefighters inside. This turns that window into the point the cool air comes in and the neutral plane on the stairs disappears and the entire staircase becomes a chimney of superheated air and smoke top to bottom, likely killing anyone who remains on the stairs.

Perhaps worth pointing out that the 12 who survived did not run into the fire. They broke a window and went downwards past the fire. From Wikipedia:

Twelve people from the rear of the train broke a window with a ski pole and, advised by an escapee who had been a volunteer fire fighter, escaped downwards past the fire and below the smoke.

I’d never taken the time to realise firefighters have to learn about physics-nonsense for their line of work. On top of having to stay really fit? That’s tough

followed the advice of a retired firefighter

The actual YSK.

Direction to go in case of a public transit fire is probably highly context dependent. The real lesson here is to follow instructions of trained emergency response personnel