After moving a site collection from one farm to another Document Set Content Types when used created folders instead of a Document Set

Here is my situation. We are moving sites from one farm to anther because we updated our Server equipment.<o:p></o:p>

After moving one site collection (This was done by backing up the site collection and restoring it in the new farm) , Document sets that were already there work correctly. Also, in this site collection there is a Content Type created at the site collection level that is based off a document set. <o:p></o:p>

Now when a new library is created, in the library's settings we add that Document set content type. Then when a
document set is created, the document set looks like a regular Document Set. The home page displays, we can upload document.

Then, when We click refresh, all of a sudden the document set look like a folder in the library. <o:p></o:p>

When I look at the Folders through PowerShell I do see that the $list.folder.ProgId is blank.I did update this to "SharePoint.DocumentSet". Now the folder acts like a document set. <o:p></o:p>

My question is:

How would I fix the content type to Create a document set every time it is used in a new library, so that I will no longer have to fix every folder that is created?<o:p></o:p>

pfcjt@hotmail.com