I will try my best at not divulging plot details.
Towards the end of the movie, Malcolm and his crew reach Mr. Universe's abode with the intent of broadcasting the recording made by (planet) Miranda's (late) lab scientist.
Just prior to this, when talking with his crew about the above mission, he deduces that Alliance probably wanted to capture River, and, thereby keep that "incident" secret.
In the first half of the movie, we see River kept having visions of reavers in her dreams only. We are not shown a scene where we can deduce Alliance was responsible for the "incident" prior to the scene where Malcolm and his crew visits planet Miranda.
In the opening scene, the Assassin shows his concern to the Alliance scientist that (the psychic) River was demonstrated in front of senior Alliance members (to show that she was a capable weapon). And because River was psychic, she could have read minds of the senior members and come to learn of "the incident", and thereby Alliance's involvement.
But how does Malcolm finally deduce this?