Hi Mike,
The index table update is automatically triggered when a post is altered (saved, updated, published etc..). Namely, when the following filters are triggered, the index table automatically re-indexes the post that is currently changed: save_post, wp_insert_post
These hooks are automatically triggered, when making changes via the plugin editor, or within any interactive editor out there. Manually changing anything via code or directly in the database will not trigger these events.
If you are using a custom code to make changes, then the save_post filter needs to be triggered, so that hooks connected to this event are fired properly. To do that, you can either update the post manually afterwards via the editor, or try running these lines after the change integrating them into your custom code:
The $post_id variable should be changed to the one that contains the currently changed post ID.