I have enabled close caption for HDS, HLS, RTMP for VOD playback. Also, placed a sample.srt or sample.ttml in the content directory. To test the functionality I have tried Flowplayer, Strobe Media Player and Wowza Test player. The flowplayer and Strobe Media Player does display the captions.
While performing my tests I have found that with HDS I see the Stuttered playback. The captions gets displayed, then video pauses for couple of seconds, then it resumes. The Wowza Test player also doesn't play the video correctly (the same stutter playback can be noticed).
Next, I tried the HLS and RTMP playback and found both work smoothly. The wowza version I am using is 4.0.5.
Also, once I disable caption from wowza server, it plays HDS smootly.
So in summary HDS with Captions Enabled is not playing smoothly.