Octane is totally unrelated to deflagration rate (the speed of burning). Different mixes of gas such as avgas might have a different rate of deflagration, but it is controlled in a method outside of the chemicals that relate to octane.
Meaning, higher octane fuels might burn faster or slower. The octane doesn't matter.
People think octane relates to the grade of gas. OCTANE MEANS NOTHING unless it is too low.
Think of it like this. Deflagration is the burning of gas in the manner people usually think of, as a flame front, subsonic speeds. Detonation is when burning happens so fast, it becomes supersonic. Detonation creates a shock wave (sonic boom).
Optimally, an engine want to run as fast a burn as possible, without risking detonation or any of it's effects. Faster means quicker power application, and no, the charge does not cool down in the cylinder to the point that it is not pushing on the piston.
optimally, you want your fuel to burn quick so that as soon as the piston is going down, there is 100% force pushing it down. A slow burn results in lower pressure at that point, as the fuel is still burning while the piston is going down. thats normal, but it's not preferred.
anyway, to repeat a previous post, the additional power from 91 octane only come into play at full throttle, as autoignition (detonation) is only a problem at higher heat and cylinder pressure, and until your foot is flat on the floor, the throttle never lets a cylinder get a full dose of air, and thus even with high compressing engines such as the 1gr-fe, never needs the added headroom that 91 octane fuel provides.