JSpin Sorry for the trouble! I have confirmed that I can reproduce the problem with the Spine project you provided, so created an issue ticket for this: EsotericSoftware/spine-editor759
Thank you for your detailed bug report, I was able to reproduce the problem very quickly.
As far as I have tried several patterns, it seems to happen only when the FPS specified for a sequence key is the same value as the timeline FPS. For example, if I change the FPS of the sequence key to 30 but leave the timeline FPS at 60, it will correctly update to the next frame every two frames (even if the sequence key is at after frame 250). However, if I change both of the timeline FPS and the sequence key to 30, the same problem occurs.
It's not perfect, but if I change the FPS to 59 for the sequence keys in the Spine project you provided, it plays almost as expected. I would appreciate it if you could do so if this could be a workaround until the fix is completed.