ZeroTier hasn't been self-updating on Linux since very early versions. We found that many Linux users were using it on servers and really did not want software auto-updating itself independent of their scheduled use of 'yum' or 'apt'.
In 1.1.6+ we have finally developed real Linux packages and our own Linux package repository. The install script we created just adds that repo and installs the package, and once the repo is added it should auto-update along with other Linux packages when you do system package updates. This is expected behavior on Linux for a packaged app.
We also have people working to get this into Fedora/EPEL and Debian upstream but that's another matter, and many users might still prefer our repos since they will be updated more quickly.
MacOSX and Windows have auto-update functionality but we've been sort of gun shy about using it for the same reason. So far our policy has been to keep it around in case we ever have a critical security vulnerability that we need to force-patch ASAP. So far that has not happened.