I have the same problem,
Here is some more info to avoid anyone asking unnecessary questions.
I have 3 external drives
two of them with Mac OS Extended (Case-sensitive, Journaled) format (usb3 and thunderbolt)
the third one usb2 with an ExFAT format.
I'm having icon change problem with the ExFAT one.
the first time I tried, it changed but couldn't change it again. whatever icon re-applied showed the initial icon only.
so I removed the icon from info by the cut command, deleted '.VolumeIcon.icns', changed the drive name
unmounted and remounted, now the default icon is not changing at all.
One strange thing which I think might have relation to the problem is that Parallels Desktop shows the drive as 'Read Only', which it is not and says 'You can read and write' on the info and I can read and write.
Usually opening a png file with alpha in preview and copying it and pasting the clipboard to the drive info icon area works, however, this problem might have to do with how 10.10.5 deals with ExFAT formats.
I really hope someone can find a solution to this problem.
I am using a full spec Mac Pro and using it for music production so I'm really not interested in upgrading the OS, which is unnecessary and causes many software incompatibility problems
anyways I just changed the drive name to something else again and it fixed the problem while I was writing this post.
renaming changes the drive icon. the initial name shows the wrong icon, the new name shows the new icon.
It's crazy, well, I came up with a new meaningful name for the drive so I'll live with a NEW name for the sake of the correct icon. It's really stupid. I'm really amazed OSX still having stupid bugs like this...
I hope this helps someone.