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On the Content taxonomy project page it states the following:

“storage settings: storage is done in the CCK tables. But for many modules it’s necessary, that the saved values are also available to the core Taxonomy system. In this case it’s possible to save values additionally to the core taxonomy database table. (Drupal 6)”

This implies that there is an option for saving the information to the standard Drupal taxonomy table. If saved to the standard taxonomy table then the Advanced Taxonomy Blocks module has access to the terms. Otherwise it won’t work. I don’t know where that setting is changed as I don’t have any use for the module myself.