I sat at a couple of large airports recently, checking that my FSLTL was correctly installed and working, and aircraft were taking off on completely different runways to what was shown on FR24. I thought it might be a delay of 15 mins or more, but it seemed not.
I later found that if I changed airports and reset the injector, the models & liveries would often be from the old airport. After completely restarting it, it always corrected itself and reset back to local aircraft & liveries.