When you say that testing in the timeline is different to testing in Animate, do you mean you go somewhere and press Return or Enter, and the play head moves along? But when you type command-return or control-enter that it plays differently?
That's not unexpected. When you let the play head move across the timeline it's not doing any synching between the animation and the audio, and it's also having to update lots of other panels.
You could go into one of the full screen modes, and maybe get closer, but if it's a complex animation it will probably still go out of sync.
If you're dealing with HTML5 there's another complication, in that you can't use Stream audio, which means you can't scrub the timeline to listen to how the sync is going to work.
One approach you could take is to convert the FLA to AS3, set the sound to Stream, reposition everything so that when you scrub the timeline the animation is in sync with the audio. Now convert it to HTML5 Canvas. The sound will become Event, but when you play it in a browser it will hopefully keep the same sync you saw in AS3.
It most likely won't keep sync. But I have an answer for that too. Try the suggestions I made, and ask more questions about whatever doesn't work well enough.
Thanks so much! Changing the audio from event to Stream fixed the synch, and everything is working properly now!
But there's one more problem I have. Do you know if it's possible to test an HTML5 animation inside of Adobe Animation, and not in browser? This is something that has been bugging me.