I think you're mixing up two things.. Local index using smart search uses Lucene and stores the index files locally!
Azure search is (obviously) using Azure and stores the index external. Can you confirm which one you are using?
Can you verify the search is actually working from the admin interface?
In the Smart Search module open your custom search index and navigate to the Preview tab:
When Using MVC also verify the Web Farm syncing is set up correctly. As the smart search index changes need to be pushed to the frontend MVC site!