Meagan Longoria notes that last processed date is UTC but the Properties page is local time:
The datetime returned by this query is in UTC. My query returns 9/19/2016 7:43:03 PM.
If I go into the properties of my SSAS database, I can see this same info, but the timezone conversion has already been done for me (this server is in Central time zone).
I think that on net, that’s the best way to do it: store everything in UTC and use the presentation layer to convert those to local times.