By default you need more than 1 page or 25 records to display the filter. Here is the statement from the documentation
By default, list filters appear when the number of records is more than 25. You can change this limit by adding the following key into the appSettings section of your web.config file:
<add key="CMSDefaultListingFilterLimit" value="5" />
Looks like you only have 8 records showing in your Azure instance and your local database has more.