Remove the `"share"` mount option in the synced folder config for the Parallels Provider. With that, the file owner is not set to `www-data`, but to `vagrant`.
Run `tar` and `npm` as the `vagrant` user instead of `root`.

The Parallels Provider does not support `chown` (see https://github.com/Parallels/vagrant-parallels/issues/103#issuecomment-51479461), which `tar -x` (see https://github.com/fgrehm/vagrant-cachier/issues/53#issuecomment-27364917) and `npm install` need/run at one point or the other, if they are invoked as `root`.
Following the approach from https://github.com/Varying-Vagrant-Vagrants/VVV/pull/370#issuecomment-44260526, `tar` and `npm` can be run as the `vagrant` user, as untaring and npm are done in the user directory and don't require root permissions.