Just like CPT capabilities those of taxonomy are also customizable, in register_taxonomy():
capabilities
- ‘manage_terms’ – ‘manage_categories’
- ‘edit_terms’ – ‘manage_categories’
- ‘delete_terms’ – ‘manage_categories’
- ‘assign_terms’ – ‘edit_posts’
Since your authors only have edit_posts it works as you observe — they can assign existing terms, but not create them. You can customize capabilities for taxonomy in question and give respective capability to authors, so that they can create terms in it (but not in other taxonomies).
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