Please remember that extra database definitions are per backup profile (like all settings in Akeeba Backup), not global. If you configure an additional database in your backup it will ask you to restore it when restoring the backup.
Also note that a database is defined as a different database name (with the same or different database server hostname, username and password as your main site's database). If your CiviCRM tables are stored in the same database as Joomla!'s tables then you really have one database, just two different prefixes. In this case Akeeba Backup will backup and restore all tables (Joomla!'s and CiviCRM's) as part of its main site database backup and will not ask you to restore an additional database.
So, based on this information we have one of two possibilities:
1. You defined the extra database in one profile but backed up with another profile. In this case your CiviCRM database was not backed up. In this case you need to take a new backup with the correct backup profile.
2. The tables of Joomla! and CiviCRM exist in the same database. In this case all your tables were backed up and restored as part of your main site database backup and no further action is required.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!