Hmmmmmm -- I don't know.
don@imerabox:~/.local/share/applications$ cat chromium.desktop | egrep Exec
Exec=/usr/bin/chromium --disk-cache-dir=/run/user/1000/chromium-cache %U
don@imerabox:~/.local/share/applications$ ls -la | egrep chrom
-rw------- 1 don don 315 Jun 3 11:32 chrome-cfhdojbkjhnklbpkdaibdccddilifddb-Default.desktop
-rw------- 1 don don 310 Jun 20 11:55 chrome-gighmmpiobklfepjocnamgkkbiglidom-Default.desktop
-rw------- 1 don don 311 Jun 2 16:38 chrome-mlomiejdfkolichcflejclcbmpeaniij-Default.desktop
-rw------- 1 don don 480 May 18 09:37 chromium.desktop
don@imerabox:~/.local/share/applications$ cat chromium.desktop | egrep Exec
Exec=/usr/bin/chromium --disk-cache-dir=/run/user/1000/chromium-cache %U
But I did not ever edit any of those. In the dolphin view, the first three have icons that match the Ad-Block Plus, Ad-Block, and Ghostery extensions so I assume that's how they got in there. And they have their own little "Exec=" command line:
don@imerabox:~/.local/share/applications$ cat chrome-c* | egrep Exec
Exec=/usr/bin/chromium --profile-directory=Default --app-id=cfhdojbkjhnklbpkdaibdccddilifddb
So, I edited /usr/share/applications/chromium-desktop only. But my custom disk-cache-dir= command shows in ~/.local/share/applications/chromium.desktop, so it must be getting copied (overwritten) there from the /usr/share/applications version during the update of the package. At least that is what I think is happening. For sure, if I forget to make the edit after a chromium update, the cache will be built under ~/.cache/chromium/Default instead of in the /run/user tmpfs.