Hi,
According to your post, my understanding is that you wanted to use a group by view and combine with the Managed Metadata filtering and navigation in a document library
to show the corresponding documents with the correct numbers in SharePoint 2013.
In my SharePoint 2013, I created a view which was group by two columns and combine with the Metadata Navigation Hierarchies and Key Filters some fields in a document
library. As a result, it showed only items matching the filter values.
So, I recommend that you can follow the steps to implement it in your environment.
Step1: Enable Metadata Navigation and Filtering:
Metadata Navigation and Filtering is a Site Feature that has to be activated for this to work.
And, the Metadata Navigation and Filtering feature is enabled by default on most sites.
If it is not enabled for your site, you can enable it on the Site Features pages for your site.
You must be a Site Owner or a Site Collection Administrator to enable Metadata Navigation and Filtering.
1. Go to Site Settings and click Manage site features under Site Actions.
2. Find Metadata Navigation and Filtering in the Features list and click Activate.
Step2:
Configure Metadata Navigation:
You must have a least the Manage Lists permission level to configure metadata navigation for a list or library.
1. Open the document library for which you want to configure metadata navigation.
2. Go to Library Settings of the document library and click Metadata navigation settings under General Settings.
3. In the Configure Navigation Hierarchies section, select the field or fields you want to display in the navigation hierarchy and then click Add.
4. By default, Folders are automatically displayed in the navigation hierarchy. If you do not want folders to display, select Folders, and then click Remove.
5. In the Configure Key Filters section, select the fields you want to add as Key Filters, and then click Add.
6. In the Configure automatic column indexing for this list, specify whether you want to automatically create indices on this list to increase the performance of the
queries that users will perform when they use the Navigation Hierarchy and Key Filter columns you've specified. It is recommended that you select the option Automatically manage column indices on this list.
7. Click OK.
Step3: Set a group by two columns by modifying view in the document library:
1. Go to the LIBRARY ribbon of the document library and click the Modify view.
2. Click the Group By and select up to two columns to determine what type of group and subgroup the items in the view will be displayed in.
3. Click OK.
Step4:
Go back to the document library, apply Navigation Hierarchies and Key Filters to do a test in your environment.
The result will like as below:
There is an article about how to apply Metadata Navigation Filtering in SharePoint 2013 for your reference.
http://blogs.interfacett.com/how-to-apply-metadata-navigation-filtering-in-sharepoint-2013
Best Regards,