don't wonder anymore, Avast installs for the SafeZone its own custom version of Chromium. Nothing to do with your Chrome install.
Now keep in mind that Chromium/SZ is currently the "equivalent" of Chrome/stable version 9, so it's seriously outdated yes (as "stable" is current V10). But as said that's Chromium, not Chrome, and it doesn't auto-update. You'll have to wait for Avast to update AIS to see the SZ browser updated too.