The Algolia Magento extension supports category indexing, which makes Magento Categories searchable through the Algolia search box on your Magento website. This feature checks the addition of categories in your Magento store and continuously makes them searchable in Algolia.
Category deletion does not trigger product deletion in Magento and the extension follows the same logic. If you delete a category, it will be removed but products under that category are not removed. To remove those products you should delete/disable them.