This is the step. This is the only time your Walkman will actually read the tags.
Now as to why it reads different when it has been connected to Windows or Linux is not something easy to answer.
My guess is something at filesystem level that is ticked by a WinOS, but not a Linux. File change date? Some other flag? No idea without reading a boring MTP spec.
As I mentioned earlier, this isn’t just ancient tech that uses databases. Phones are similar with having an internal database. My old Android phone connects to a PC with the same MTP system. I copy tracks on, then unplug. It is this point the phone then looks at the new stuff and updates its own internal library.
This library is then shared between the apps on the phone who think they can play music. I use Yatse and have talked to the dev before about how my ancient phone does not correctly read the artwork some days. Nothing that app can do about the OS just being dumb.
Note - I am no expert on this stuff. Just curiosity means I reverse engineer some tech cos I want to know how it works. Part of the reason I dive into questions like this… addicted to knowledge. 
