This is reported by BBC folks:

The spec for when text track cue events should fire allows for some variation (up to +250ms) in the actual time relative to the media, and Chrome seems to work within this, but to trigger audio playback and mixing in synchronisation with the media, which is needed for the audio description use case, 250ms is too long. There's some mismatch in browser implementations, within the parameters of the specification, so this is not a browser bug, but a spec bug. For example in my testing Firefox seems to fire the onenter() and onexit() events within 10ms of their requested time usually.

It would be good to get feedback from the Chromium team on the practicability of reducing this threshold prior to requesting a spec change. It also has an impact on subtitle and caption display timing accuracy. I should point out also that this was discussed in the Media and Entertainment Interest Group and a breakout on data cues at TPAC; one proposal was that the desired timing accuracy could be set on the cue itself.