Let's see what your page says:The Red Genosect and Myuutwo leave Pokemon Hills and have a brief aerial battle during which Myuutwo gets defeated. After being unconscious for a while, Myuutwo wakes up, heads over to Pokemon Hills, "awakens," and then starts a second battle.
This transformation in-movie is obviously the character's awakening as described in the movie's title. I don't know how you could have possibly misinterpreted that.
Unless your synopsis is inaccurate, Mewtwo doesn't battle Genesect the first time; it tries to reason with Genesect but gets blasted away unexpectedly. After it regains consciousness, it finds Genesect again and transforms, having realized that it has no choice but to fight. My interpretation of this is that Mewtwo could have transformed to begin with, but it obviously preferred to avoid a battle. If Mewtwo regaining consciousness is its awakening, then this is a new low. Even Keldeo unlocking its Forme was a lot clearer than that; it happened when Ash told Keldeo to become more resolute, making it flash back to its mentors and realize that it had to save them. In this case, Mewtwo doesn't even try to battle Genesect before transforming.Suddenly, Myuutwo bursts onto the scene asks the Red Genosect to follow it so they can talk. The Red Genosect responds by charging at Myuutwo with Extreme Speed, hitting it in the chest and sending it flying through the city. Myuutwo eventually crashes into a wall and appears to loses consciousness.
Elsewhere, Myuutwo regains consciousness. The man-made pokemon rushes back to Pokemon Hills to ask the Genosect to stop one last time, but it soon becomes obvious that they have no intention of doing so. Myuutwo closes its eyes and begins to glow until, in a flashy burst of power, it transforms into a new "awakened form"! Myuutwo explains that if it can't stop the Genosect with words, it'll have to use force instead.
Even if my interpretation is wrong, at the very least Mewtwo should have some on-screen moment of revelation when it loses consciousness.