I thought they did. Last time, everything happened within a week, but it started with a vision. I haven't had one since then and I've been using my rewind, and... nothing. The weird weather stuff with the frozen people and animals started before I showed up. We haven't had a snowstorm or heavy rains or anything like what happened in Arcadia Bay.
I'm not saying there aren't any consequences, but I don't know what they are anymore.