I have found that the issue can be resolved by manually changing the audio channels' time stretching mode to "stretch" rather than "Auto", however it is very frustrating to make this change manually for every channel in my project.
In FL Studio 12 I did not have this issue and many of my audio samples used "Auto" time stretching mode.
If my explanation is not clear please check the attached project file which illustrates the issue. If you play from start of bar 3 or before, everything is in sync. If you start playback from anywhere between bar 3 and 5, suddenly the audio plays out of sync. And the offset varies depending on where playback begins.
I hope it's not too hard to fix
-Znernicus