All times shown are in your own time zone.
The other players se all times in their local time zone
Because of this you may need to give some reference point when you are telling other players about some event. Instead of saying "see the log entry at 02.41am" you can write "see the log entry at xx.41 about 5 hours ago".
The game itself are in the UTC time zone (or GMT, without summer dayligt saving) and Daily events and such always starts at midnight UTC. Please note that in some cases there be an another starting time, but normaly the game will have base time.