By default, `watch` runs your command with `/bin/sh -c '...'` so the output you see is how `/bin/sh` interprets the `time` command. Your `/bin/sh` apparently doesn't have a builtin `time`.

To run the command with a different shell, use the `-x` option to get rid of the default, then add your own explicit invocation of the shell whose builtin you want.

 watch -x bash -c 'time ls'
 watch -x zsh -c 'time ls'

No matter how you run `watch`, the command you're watching is not a child the shell that ran the `watch` command, so that shell's settings aren't directly relevant.