December's presence (and presence of mind) was not coincidental. Ever since she was seven years old and her mother walked out of her life, she's been able to see the future. In this case, she knew the man was about to drown and when Nick did nothing, she intervened, saved the man, and altered the timeline. But as she did so, she foresaw that she and Nick would fall in love and that shortly thereafter he would die.
To avert that preordained outcome, she tries to avoid him altogether, but Nick can't stay away and she doesn't want him to do so. In fact, not only do they fall in love, but he promises to help her find her Mom -- a search which sets off a tragic chain of events, not all of which are foreseen.
In brief, it is an often confusing story with a fascinating circularity. So many subplots and they all eventually tie up together. This is complex and madly clever writing and a definite recommendation for people who enjoy stories about fate. While I enjoyed the story, I was less engaged by the characters in that story, finding it hard to really like either Nick or December. And was also disappointed that some elements of the story (like Nick's dyslexia or a school bully with sexual predatory behavior) were so underdeveloped -- a predictable problem in such a complex story.