I second this product suggestion -- and not just for times displayed in the log. If I change or review a program, times should be in the Rachio's time zone. After all, those are the times that will be experienced by someone who is on-site watching the sprinklers run.
As you say, it might make sense to have a setting in the mobile app to select between Rachio and local time zones. It should apply uniformly to log entries, program settings, and anywhere else that times are displayed or entered. To emphasize how times are being interpreted, I suggest that the time zone being used should be displayed anytime the controller and the mobile device are in different time zones.
Just out of curiosity, how does Rachio know the controller's time zone? I don't see an explicit setting for that, though there are settings for Zip code and GPS lat/long.