Please Note that I only have xmt sidecar files associated with my NEF files.
By @Gordon & Susan0D4C
Normal, xmp sidecar files are not saved for jpegs edited in ACR, the same data is stored directly into the metadata header of the jpeg format (and other formats). The necessity for raw files to use sidecars is due to the fact that "raw" are never overwritten, which means you have to use a procedural editing: unchanged original with change recipe.
So, the usual workflow is to start with the raw editor in non-destructive procedural mode, then, if needed, follow in a pixel editor like Photoshop, Elements or a third party editor.
If you re-open in ACR a jpeg/psd/... produced after a first raw stage, the process involves raw > pixel > raw > pixel editor stages in which any special profile may have been "cooked in" in the pixel stage. That is how I suppose you have met your present issues.