I originally published the temporal layer with the correct time zone for the data.
Publishing this to an ArcGIS for Server 10.3 instance, I can see that this has flowed through to the REST endpoint:
The Time Extent of the time data, is 5am to 10am on 27/04/2015, AUS EST.
So the above UTC time is technically correct.
Adding this layer to my app, and using the standard time widget provided in the Esri JS API, I have some issues.
Viewing the app here in Melbourne (same time zone as service), everything is good.
Can see the labels are correctly populated from the service, spanning 5am to 10am.
Howeverer, viewing the app from a machine in a different time zone, and it seems to use their local time zone:
I saw some other posts where they mention to do things like publish in UTC and add/minus the relevant number of hours?