This organization you described is not the standard of Wordpress. Usually when there are multiple Wordpress installations within the same database, a prefix is used for each installation. There you have to identify the tables by prefix and export them separately.
If you still have access to each client’s Wordpress the best is to use the Wordpress exporter himself to move the websites. It will take care of the database and all attachments and you will not need to worry about the way the database was organized.
Depending on the site size and server performance, the import may give timeout or memory error. In this case you have two options. Either separate the export xml into smaller chunks or use a backup plugin to transfer the database.
If using a backup plugin, I indicate the Backupwordpress. You need PHP greater than 5.3 to run. Just back up the database and it will create an sql file with only the tables related to that site.
You can send the print of the hierarchy, organization of these tables, there in phpmyadmin?
– Lollipop