Here's my workflow to create a VTT for Vimeo and Youtube. Just substitute the VTT export for SRT at points 4 and 5.
Closed Captions to Youtube & Vimeo workflow
EDIT: Ohhhh no wait, you mean you build your subtitles in the text generator rather than the closed captions generator? That's a bit trickier. I don't know of any way to shift titles over to caption land without redoing the whole thing, and I'm guessing you don't want to do that. Anyone help out