If you're loading the XMP files into Lightroom, try loading them into Photoshop:
1) Select a RAW file along with the matching XMP file you received from your editor.
2) Drag both files into Photoshop. This will open Camera Raw.
IF THE EDITS APPEAR CORRECTLY:
You can either bring all the images into Photoshop and load them this way. If you prefer to work in Lightroom, create a brand new catalog, and re-import the RAW + XMP files into it.
Your original LR Catalog was having trouble reading the new XMP files, and was referencing a previous version of the file.
IF THE EDITS STILL AREN'T LOADING:
Get in touch with your editor, as the XMP files didn't export properly.