Combustion reactions are complicated even when they result in simple products
Part of the problem with answering the question "at what point are water and carbon dioxide formed" is that the reactions occuring in combustion are very complicated and not at all well represented by the simple versions shown in the question.
We can say for sure that the picture where all the components are atomised and then recombine is not the way the reaction works. This simplistic idea is part of the reason for disagreement on the reddit thread.
It is an incorrect view for many reasons but mostly because the reaction doesn't all happen at once. Take petrol (that's gasoline for americans) engines. The initiation of combustion is started by a spark and then (relatively slowly in chemical terms) progresses through the rest of the fuel/air mixture (if it were very fast the engine would explode rather than smoothly driving the cylinder, if it were only a little too fast the engine would "knock", damaging the cylinder). So we need to think–even before considering the detailed chemistry–about the (slow) steps involved in the reaction.
The major steps involved in most combustion reactions involve radical chains. Though the full detail is not understood (though this answer gives some more detail), it is thought that the initiating step involves a hydrocarbon reacting with an oxygen molecule to give a hydroperoxide radical and a hydrocarbon radical. Very simplistically this looks like:
$\ce{O2 + CH3(CH2)nCH2-H -> HO2. +CH3(CH2)nCH2.} $
But neither of those radicals is stable or long-lived. In an environment flooded with more hydrocarbons and oxygen, they can both react further to give more products and more radicals. For example, the hydroperoxide may also fall apart to hydroxide radicals which can react with parts of other hydrocarbon molecules to give water and yet more radicals. In the early stages, most reactions create more radicals; later in the process some radicals can combine into stable products (like water and carbon dioxide). Once the reaction is started it can be self-sustaining as the formation of those stable products release a lot of heat, enough to keep creating new radicals and new chains until the source hydrocarbons or the oxygen is depleted.
So, even thinking about the detailed, step by step, chemical reactions suggests that the process is messy. Even early on in the process some final products are being created, though this continues until the fuel/air is mostly used up. if you plotted the amount of final product over time you would see some very early and a rising amount until the reaction had finished. It is pretty meaningless to ask "at which point" the products are formed.
In short, the initiation does not "atomise" the components: it creates radicals (this doesn't need as much energy input as "atomisation"). They can continue to react creating chains of yet more radicals and some chains can stop when stable products are formed, even early in the reaction. The net reaction releases enough heat to sustain combustion while fuel remains. Final products start to form early in the process and continue to be formed until the air and fuel have gone.