Warning: Spoilerish Stuff.
While I have not seen The Odd Life of Timothy Green myself, taking what I know about the plot and the impassioned cries of these children, I think I can put 2 and 2 together.
Timothy Green builds an organic time machine out of his own leaves and goes back in time to the Titanic to save Jack and Rose from their wet, frosty predicament and bring them back to our time. Unfortunately, they get hit by a teenage girl who was texting while driving.
Sad stuff, indeed. I can see why these kids are so touched by the film.