I'm not even sure if the linux version of FF has an auto-updater. And even if it does every distro I've ever used (Debian, Ubuntu, Fedora, and currently Arch Linux) must disable it, because I've never had FF try to auto update on linux.
OP in this thread seems to be using that installer with automatic updates, and then disabling it by hand, since when updating via a package manager you don't run into this issue.
It does if you download it directly from Mozilla.