Well, the movie is structured like a Mobius strip, where Cole's actions inevitably lead to his younger self witnessing his own death, the trauma and memory of which lead him to cause that death by seeking out Railly and running off to the airport. From the point of view of a camera that followed around young Cole until he aged, went back in time, and died, then glided back to young Cole, this cycle is infinite. Cole has met Railly an infinite amount of times and it always ends the same way.
So, the hokey explanation is that Railly remembers Cole because in a skewed metaphysical sense, she's always known him. Cause and effect runs both backwards and forwards in time throughout the movie, and so Railly and Cole's memories appear to cause ripples both backwards and forwards in time.
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