Flights generated by FS Traffic will activate at the time stated in the Traffic Control Centre "Schedules Manager". They will then run through their pre-flight routines (connecting the jetway, baggage loaders, etc) before pushing back from the gate. This process can take up to 15 minutes depending on how many ground services interact with the aircraft. To speed up this process, you can go to Aircraft Manager > Ground Services > Set No Ground Services > Save Changes. This will remove all ground services from the aircraft, allowing them to push back within a few minutes of their scheduled departure time.
It is also worth considering that FS Traffic uses the in-game time when activating flights. So any changes to the in-game time after loading into an aircraft can prevent FS Traffic flights from activating flights. For example, a flight that is scheduled to depart at 10:00 will not activate if the in-game time is changed to 16:00.
For further information on how you can use the Traffic Control Centre to customise your FS Traffic experience, we would recommend having a read of the FS Traffic manual.
Hope that helps.
Mark - Just Flight