Unfortunately (in this case) this isn’t the case, as others have established by now. The best you can do is some type of workaround to get the or close to the information you are looking for, e.g. what @dpfeilsticker suggested. I hope you can live with that, because it would be a shame if this was a dealbreaker for your use of restic!
Another type of workaround might be if the --json -vvv options outputs a line for each file when that file has completed backing up, and you can pipe this to something that picks out the filename and also adds a timestamp - if this works it should give you the timestamp for each file. Try it and let us know 
Here’s an example of a JSON line:
{"message_type":"verbose_status","action":"new","item":"/doc/man/restic-find.1","duration":0.000678317,"data_size":3878,"metadata_size":0,"total_files":0}
I’m not sure if this type of line is output when the file has been sent or if it’s output when the file has been scanned.