Looking at your screenshot, I think the timeline 'swimlanes' and the anomaly charts are in fact both using the same timezone.
It is important to note that the data in the timelines is bucketed into intervals, depending on the time range set on the dashboard and the bucket span of the job(s) selected. So in your screenshot, each section in the swimlane represents four hours. The colour of each section indicates the highest score seen in that interval, which in your case is an anomaly at around 18:30.
The anomaly charts below however are always plotted using an aggregation interval equal to the bucket span of the job - to ensure we show the actual anomaly in the data and don't get any 'smoothing' effects from a longer aggregation. The time range of the selected timeline section is indicated by the central grey shaded region on the anomaly chart - spanning the four hours of the selected job here. So the grey section in the chart starts at 15:00 on September, the same as your selected timeline section.
I notice that the date axis labels are using different time formats - "15:00" in the timeline, but "3PM" in the chart. We will look to address this in a future release, as well as the fact that we don't follow the Kibana dateFormat.tz setting when it is set to something other than 'Browser' as I mentioned earlier.
Hope this helps.