With MILD, why does my mind not realize that it´s a dream as soon as the dream starts?

I have had some 12 or so lucid dreams, through MILD and ADA, and I want to understand more about the workings of it.
So, there I lie, in my bed, dreaming, when suddenly, my mind seems to think it is appropriate to stir now and realize: oh this might be a dream. There would have been enough dreamlike things to trigger lucidity along the way, why does lucidity not kick in straight away?

As far as I know there is not a definite scientific answer to this question that can be proved beyond a doubt. From what I have gathered (and I am no neuroscientist), it comes down to part of your brain being put in "low power" mode. Specifically the frontal cortex. This causes your reasoning and logic skills to pretty much go out the window. (I've heard this is also the why reading numbers and letters in dreams is difficult or impossible)

Without that you are not very likely to recognize the unusual or impossible dream signs. You accept everything as totally reasonable.

The "M" in MILD stands for "mnemonic" and that's the key to it all. With MILD, you develop a memory-based association that triggers when the trained stimulus is provided. Actually, with practice, you create many such associations, all overlapping and interrelated. And more specifically, the type of memory we are dealing with is called prospective memory. When the trigger is activated, you remember to question your state and discover that you are dreaming. This is how you can overcome what RebelSeven called the "low power" mode, because prospective memory remains available enough to still function.

But... the trigger system still needs the stimulus, so it doesn't just happen immediately. With practice and repetition, you can strengthen your existing triggers. And with some creative thinking, you can examine your own thought patterns and past dreams to find new triggers. Overall, you want to create a wide and reliable set of mnemonics so that you can become lucid more frequently.

The mind is very much open to suggestion while you're sleeping. If you regain consciousness in the middle of the dream, you're essentially hypnotized by the dreams suggestive power until you snap out of it with a counter suggestion that you are dreaming.

In the dream state, our mind is operating under a layer of fog and dullness, and access to memory is impaired. That's why daytime LD practice focuses on building strong awareness and access to memory, so that our "base level" of these fundamentals is high enough to still be able to get lucid in the physiological limitations of dream state. It's also why WBTB increases chances of lucidity, it puts our mind into "waking mode" and when we return to sleep we don't have quite as much of the fog & dullness as when we're emerging into REM from deep sleep.