Video with Captions play in Safari, but not anywhere else?

No one is going to have a clue as to what you are possibly doing wrong. Because we cannot see what you are doing. Posting an example of the project and explaining your process would help.

Aside from that my experience with closed captions in most browsers has been spotty but I am no expert and only really got involved with them when writing this

( which probably could do with updating - I think when I last looked at a few months agao Chrome works and Safari did not. )