It depends on the default profile SexyMap is using. It can either use the same default profile for each character, or a specific character profile. In the latter case you might think it is not working but all you have to do is to go to the profiles tab and select the same profile (e.g. "default") for all your characters.
Actually, it will work almost exactly the way I described it. I guess I just didn't try hard enough. Chinchilla has incorporated an elegant solution to this by scaling the Minimap children inversely from the Minimap itself.