I may be wrong, but from what I've seen and read so far, there won't be separate time zones.

Including it in game, likely wouldn't add anything helpful/positive to the game play either.

Thanks for the answer

I speculate that other continents may have different time zones. Since there will be no fast travel, no global chat, and the technology available will probably not progress to long-distance scheduled railroads, there will probably be no need for concern.

I found this sentence inside the Production Update: From Pre To Alpha of the 3rd of August

The world currently also has data about the temperature, weather, and time of day where you are.

So this makes me think that there are Time zones. So people on the west side may read the stars to guess their fate before those on the east come to invade them ;)

Given the size of the continents I would suspect that there would be a slight difference in sunrise and sunset depending on where you are. Even more so once the other continents are added.