Following-up on this:
There is no API provided for modifying the timestamps on the VTT. However, you could create your own processing on the VTT to modify the timestamps per your requirement.
We do not have a sample for caption reprocessing, just to let you know- there are online caption editors available that can accomplish this. Another possibility is using a text editor, although there are specific editors tailored for VTT files.
I have relayed this feedback internally to our product engineering team.
If you wish you may share your feedback on Uservoice - All of the feedback, you share in these forums will be monitored and reviewed by the Microsoft engineering teams responsible for building Azure. Additionally, users with a similar request can up-vote your post and add their comments.
Thanks for your understanding and cooperation!