The following statements are true:
watch runs the command in a new shell, sh.
.bashrc aliases ls as ls --color=auto to enable colours.
sh doesn't inherit or use bash aliases.
So when watch runs ls, it's not asking for colours, it's just running the plain old version. You can circumvent this but—as aditya points out—you also need to enable colours on watch for it to process them properly.
A working example for ls is:
watch --color -- ls --color=always
If you don't pass --color to watch, you'll see a bunch of ugly colour codes inline.
ls --color is interpreted as ls --color=always.
ls --color=auto does not print colour in watch. This suggests that it's inferring colour support from the terminal itself.
For more on the reason why, we can test if the watch shell thinks its a real terminal:
$ bash -c '[[ -t 1 ]] && echo "real terminal"'
real terminal
$ watch -- "bash -c '[[ -t 1 ]] && echo "real terminal"'"
# ... nothing.
I suspect that some applications are looking at that (or similar) to tell if they should turn on colours or not.