I think Julia is just passing the tilde without interpreting it.
The git and sh -c commands are interpreting it.
Though on my system, neither version interprets ~ as home directory—both of them create a ~/tmp folder starting from pwd.
EDIT: Tried it on the second computer, and the sh -c version works properly there (again an issue with different build tools). The specific sh command is bundled with git, and it interprets ~ as the home directory. This can be verified by running where sh and sh -c "~" in cmd.