As you upload the files with the extension already included in the file name, the file is getting uploaded as the same. The Mass File Download app only concatenates the extension ".extension" to the file name.
So for eg, if you upload the file with the name a.pdf.pdf, it will be uploaded as a.pdf as the file name and file type set (internally) as pdf. When this file is now downloaded via standard SF or MFD, it will download as a.pdf.pdf
Hence the issue is the nomenclature used while uploading files, if you upload files with two extensions then while downloading too it will download accordingly only.
Note - To avoid this issue, try uploading the file with one extension only i.e. a.pdf; now MFD/SF download will download it as a.pdf only.