While that is good, the problem is that, I assume, the subtitles were synced to the m4v's you have that are variable frame rate. But since the nominal, and I assume average, frame rate is 23.976, I would expect minor variations in subtitle sync, not 3 seconds.
Encore sees your file as 3 seconds shorter than its properties as gauged by (looks like) media info? I would try to clean up the frame rate outside Encore, so it is more likely to have the subtitles sync.