If you have any VaultWiki addons installed, disable those first because they aren't compatible with the new version. Then, download the ZIP-package again and go directly to /vault/install/upgrade_250.php?step=3
The product-XML should be ignored. The template edits are installed automatically if you use TMS. Otherwise, ignore it.
You probably won't have to change anything in the new Namespace Manager, but you should still check to make sure it looks okay.