The timeframes that Responder has in its database are not displayed correcting when viewed via an Outage Map published through ArcGIS server.
ArcGIS server expects all the date/time fields to be in UTC format, and the browser/clients then transform them into the local timezone when displayed. Most of Responder does not use UTC format and will create a problem if viewed through ArcGIS server.
To work around this, a view can be created off of any table that you want to access through server with date fields shifted back into UTC format. These fields can then be displayed in ArcGIS server instead of the actual tables.
For example, you can create a view, such as in the example below, to show date fields on the time_restored field if you are 4 hours behind UTC time. You set the date 4 hours ahead: