This is a weird problem that I don’t think has any bearing on anything but in case it does. On the events page in the back end of my site the event is listed as having a start date of June 2. The event actually begins on June 4. On the edit event page, in the event datetimes section the start date is listed correctly.
Usually, when the dates are incorrect like that it means something else on the site is loading and changing the server’s timezone from UTC (which is what WordPress, and therefor Event Espresso expect it to be set at).
Do you have any other plugins that deal with data in any way?