Some burning off of the gases from the wood, (especially in the newer EPA-rated stoves) occurs all the time anyway, as part of the normal process of the burn, in a tight stove system found in more contemporary stoves.
That being said,.........as you adjust your damper (air) controls down, reducing the amount of fresh air introduction, the gases build up more readily within the firebox and burn again. The evidence of this is found in the tubes with the series of holes in them, above the burn.
You will see a marked difference in the flow and structure of the flames, and even see some color variation to the flames, as the gases burn.
I have two tubes on the top of the inside of my firebox, and I often see the back one, more prevalently than the front one, showing signs of flaming, out of those holes. This along with the change to the behavior and characteristics of the flames, are my evidence that the gases are undergoing a second burn.
Let's face it, .......the secondary burn of the gases is designed to be a pollution reduction tool. You are doing the environment a favor, and your neighbors by reducing the amount of air quality pollutants you are putting in the air. Since the newer stoves are designed to accomplish this benefit, it became a part of "burning wood for heat" process, by default.
Rather than focus on how much evidence I have that the secondary burn is occurring in my particular stove, I focus more on the burn itself, for the sake of the burn. I concern myself with how much heat I am capturing and putting into the house, as opposed to "out the chimney." Be more attentive to that, and learning to maintain a fire, than worry about how efficient or how much evidence of efficiency is present with the secondary burn. Certainly I care about the environment and want to do my best to "tread lightly" as they say, bit I didn't become a wood burner to be a tree hugger. I became a wood burner because I'm basically a person who wants to save $$$$$$.
Your stove is designed to accomplish a secondary burn, so you can see the evidence in varying degrees depending on hot how a fire you burn, and how much you turn back the air. Believe that it is doing so, and move on to other aspects of the burn.
-Soupy1957