In Magento, what is the expected behavior for parent / child attributes (bundle, configurable, etc)?

For products with parent/child relationships, if the parent product does not have any values for the attribute and the child products have value(s), the array of child product value(s) will be sent to Algolia. 

If the parent product has a value, only that value will be sent to Algolia. 
 
You can't modify this behavior in the admin dashboard of Magento; however, you can modify the backend indexing behavior as indicated in this documentation. 

You can also use a completely customized version of the extension (as outlined in this guide) if the modification above isn't sufficient for your use case.