ACR stores the data in an XMP file when changes have been made to a RAW file. What about DNG, JPG's and TIFF files? Where are the changes made in ACR stored for these files?
The data is stored within the file itself for dng's, jpg's and tiff's. Its embedded. The XMP Specification document from Adobe
(link goes to XMP Spec pdf) describes exactly where, within each file type, that the data is embedded.