The rule in the PHB states : (emphasis mine)
While traveling for an hour or more in your favored terrain, you gain the following benefits:
The way I read this and how it should be played RAW
When a party with a ranger in his favored terrain starts travelling, the first hour of travel the feature is not active and will activate only starting at the 2nd hour of travel ? So they could become lost during the first hour of travel if the navigator fails a survival check. If they stop travelling for some reason, then they need to again make surival checks for the first hour and then Natural Explorer will quick-in again at the 2nd hour.
Is that correct (as per RAW playing mode) ?
NOTE: We are not playing with UA rules.