should barline ending a Fine meausre be special?

None of these show why the playback doesn't stop at the fine, a real score would be needed, not images of it.
The Fine image looks stange though, the Fine text should right-align to the end of the measure, so I suspect an issue there (and a normal barline at the last measure of the score).
The barline certainly has no bearing here, playback-wise. I'd use a final barline there though.

As mentioned, we'd need tyo see the score to understand what's off - my guess is somewhere your repeats don't match up correctly, or you aren't using a DS or DC al Fine, so there is no reason it should stop.

But for the record, there is no real requirement for a double bar at the Fine, but if it's a place that is a natural end of phrase anyhow, I recommend it. Gould actually says to use a final barline there, and indeed, many editors use that convention, but FWIW, I prefer a think double bar,