And if the subtitles are in sync with the ProRes, then they should be in sync with the DCP.
The (srt ?) subtitle files have not the info of the framerate on them. On cases like .pac, etc. usually there is a "zero" subtitle, the first that might not appear but for a frame, which has the information about the subtitle, the video etc. that one might need.
So, given the lack of framerate on the subtitle file, there is no initial value for the subtitle on that field.
Yet, if the DCP project you have is for a 25 IPS and you enter " 24 ", that the subtitles were made for 24 IPS, then DCP-o-matic will speed up the subtitles, to fit an acceleration of 1/24. (And, thus, change the framerate, from 24 to 25.)
If the video was already 25 IPS and you indicated to the program that the subtitles were made for 25 IPS, then there shouldn't be any change on the speed of the subtitles.
Also, if you were to open the ProRes with -say- VLC, and added the subtitles (either by Menu > Subtitle > Add subtitle file.. or by dragging and dropping on the player the subtitle file, while the video is playing) the subtitles should be playing in sync. In your case, at the same time the burned-in are playing.
Now, if that is the case, and if you used a similarly created ProRes without subtitles at first, that would play correct with the subtitles on the hypothetical VLC, then the DCP should have the subtitles synchronized as well. So, it might be some glitch, a pépin, if you will, on how DCP-o-matic is interpreting. I would trust Carl with that, as he suggests.
If it was me, and if I had the time and resources, I would try the following to satisfy my curiosity:
I would have exported a ProRes with no subtitles burned in.
I would have checked the subtitles' file with the ProRes, to make sure it's on sync.
I would have made a DCP with no subtitles. There would be a warning to make SMPTE DCP, I guess you haven't made an IOP/interop before.
I would have checked the subtitles (like if I was to make a VF > Version File with only the subtitles, not to confuse French version). If the subtitles were O.K., I would have made the VF, and check it with the DCP-o-matic player.
If the subtitles didn't look O.K. while making the VF, I would have used DCP-o-matic to export the DCP (with no subtitles) to an MP4 file, setting the " quality " to a high number -> low quality and bandwidth and check the subtitles with that MP4.
The ProRes master and the MP4 should be the same, in terms of timing. Therefore, the subtitles should fit both.
If they don't, then the process affects the timing of the video.
If they do, then the subtitles are misinterpreted by DCP-o-matic.
As I try to make sense out of that all, I thought about another thing for you to try:
You said something about .srt. I suppose that the subtitles' file you have in your hands is an .srt file.
I would try to open it with -say- Subtitle Edit or, if you work on a Mac, with Subtitle Edit online. Then, make a minor change, just to make sure that the file will not be kept the same. For instance, change a space somewhere, and then save again as .srt.
Then, try to check that file with DCP-o-matic.
The reason for that is that, once every now and then, a subtitle file gets some formatting that is extraordinary. And that could later create problems. I know I have had such problems that were solved in such a manner in the past, making subtitles for streaming (.vtt). They wouldn't ingest, until I would re-open, make a small change, save fix that change and save again... magic.
P.S. I see that Carl also wrote while I was writing all that.