Yes, the time shown in weather maps is your local time (LT) even if you scroll the map to other regions.
But if you choose a location to display its local weather, then the time is that of this location. More explanation
@Bonito in the detail of the location is shown the time of the location you are looking at. So if you open the detail of Sydney than in detail is Sydney's time zone. The bottom red calendar shows your computer time, so in your case Copenhagen's time zone.