The question is what do you mean by the word "update".
You can update an extension to fix bugs or you can update the content of an extension.
If you want update the PHP code of the extension, see the chapter 8 of the user manual that explain the difference between an update and an upgrade.
The update of an extension generally mean install bug fixes.
The upgrade of an extension means that you may have an impact on the DB layout.
The update can be installed only once.
Concerning the upgrade of an extension, you have to re-isntall it in each website to have the upgrade processing performed and modify the DB layout according the specific rule present in the extension.
If the update means modifying the content of an extension - in example add a user that you want to see automatically added in another website, in this case, this mean that you want to share the content of extension.
In this case, you have to share the extension to have the same content between the websites. The sharing of user (but also true for sharing of extension) is illustrated in video 16.
www.jms2win.com/en/tutorial#jms12x-16