Sorry, I probably could have explained it better. The past catches up with the future. Alex changed the future by staying alive and going to the Lake House at that moment when he knew Kate would be there.
The party's involved in a time travel/dimension effect do not lose their memory (or at least that is the way it is always portrayed in books and movies). So the future Kate still knows everything that has happened up to the moment when the Alex (that also knows everything) arrives. Kate still knows that he had died and now he has no longer died. People who don't know anything about the time travel (like Henry) will no longer think Alex died because they are not involved on the magic effect. Henry is oblivious to the magic events and thus his timeline does change along with his memory of Alex.
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