Dumbledore and Snape are the only two people who can accurately state when Snape turned away from the dark side. They are lying. Snape actually turned many months earlier, before this supposed “prophecy” was made by Trelawney.
In fact, there was no actual prophecy. Dumbledore made the story up in an elaborate scheme to trap Voldemort. He planted it in the Department of Magic and got Snape to alert Voldemort. The prophecy was intentionally vague, anything specific would have aroused Voldemort’s suspicion. But Dumbledore made sure it was specific enough. Neville or Harry. He hoped Voldemort would come after Neville, the one with Auror parents. The Longbottoms had been captured and tortured, Neville had every reason to avenge them when he grew up. Dumbledore was ready. But something unexpected happened. Voldemort went after Harry.
Harry parents were killed. But Dumbledore realized that inspite of the great misfortune, there was a silver lining. The power of love had been invoked. He knew Voldemort would return but he saw another opening. A larger plan was put in place to prepare Harry for the final battle. Through the seven books, we know that plan succeeded.
The important point to note is that the supposed prophecy was self-fulfilling. The events it predicted came to pass only because the prophecy had been made. The fact that prophecy had been made caused it to come true. Dumbledore was a master of the game. In the real world, we call it “reverse psychology” :D