Keycool 84, different function/media keys mapping between wired and wireless mode

Does anyone use Keycool 84 as their keyboard here? I just found out that function/media keys mapping are different between wired and wireless mode. Wireless mode is as documented, but in wired mode not only they default to media instead of function keys, the mapping is also different from the documentation. Looks like either the xkb or KDE itself has their own mapping, as xev does report different event when the same key is pressed in wired vs wireless mode. Any way to make this consistent?