Are the flight times listed in Deem and on my itinerary local to the place of origination of each flight or are they local to my home?

Online booking tools such as Deem or Concur, as well as all Travel-On itineraries will always use times local to the flight. Thus, flight departure times are always in the time zone of the departure city and arrival times in the time zone of the arrival city. Be aware though, that some email/calendar programs will also display the times local to time zone you have set or even where you are when you access the email/calendar.