Where does drush store the different module versions for a multisite installation?
If you are using a multisite installation with shared modules stored in sites/all/modules, then Drush pm-update will also put the new modules in this same shared directory.  This means that you must also run updatedb on all of the other sites that share the same module code, as all of the sites will need to be upgraded at the same time.

It is far more convenient to use a single-site installation, and give every site their own complete copy of Drupal core + contrib modules, as you will then be able to update each site independently.  Fortunately, splitting up a multisite install is as easy as cloning your Drupal files, and changing your web server virtual hosts configuration file to point at the new site's location.