iTunes uses Gracenote database to identify inserted physical CDs, and last I checked, WMP uses All Music.
You can submit the CD info to Gracenote directly inside the iTunes app, but it takes a few days to go live for other users. Since this concept uses a “CD fingerprint” based on the number of CD tracks and their respective times, it’s not uncommon for something like this to happen in iTunes. Especially with CDs with fewer songs as there is more likely to be a match as opposed to a CD with more tracks.
Step 1 would be to learn which media player your client is using so you can put that fire out first and then the rest later.
It’s debatable whether this is the job of the mastering engineer or the record label/management which with independent artists is not really a thing anymore.
I offer submission to Gracenote Database to my clients for a nominal fee.