Right now there are 2 ways to update your extensions. If you have installed them via your distro repos, extensions will be updated with a system update. If you have installed them through extensions.gnome.org you have to visit that page again, navigate to your installed extensions and hit the update button (the green button with the up arrow).
Well, that isn’t “how the things should work” specially in a Linux Box that everything gets auto-update. So, in three point six we get an auto-update functionality, another small detail that will make Gnome more polished.
Note: Installing extensions via our distro package manager will place them under “/usr/share/gnome-shell/extensions ” and they will be available on all accounts in a multi-user system. Installing extensions via extensions.gnome.org (that is recommended) will place the extensions under “~/.local/share/gnome-shell/extensions “ and they will be available only for the current user.