^ Been a while since I did read the movie, but I think the events in the movie are the same. From Henry's POV he first meets Claire as an adult, and she already knows him, and tells him over dinner about the first time she met him; in the meadow. So then later when he travels and appears in the field he knows what's going on and who the little girl is.
And then back in the present he tries to look at Claire's old diary as he wants to sync up the dates of when he will appear in the meadow.
Love the Alba scenes in the movie too, esp when there are two of them, the 10 year old and the 5 year old version together, that's a really cool concept well executed.
Oh yeah, and not gonna deny I got a bit welled up in the cinema in the scene when he meets his mom on the train. I mean, my mom's not dead or anything, but just imagining what that would be like, or even going back to see my mom with me as an adult, and her when I was just a kid, the old her, what that would be like...