I am using quotation marks like this:
Joshua Abraham Norton, who liked to call himself "Emperor", dressed in elaborate clothing.
The strange fish, which scientists call a "coelacanth", lived in deep underwater caves.
My question is, does the quotation mark around these words go inside (as I've shown above), or is it correct to put them outside punctuation, as below, which my proofreader wants to change:
Joshua Abraham Norton, who liked to call himself "Emperor," dressed in elaborate clothing.
The strange fish, which scientists call a "coelacanth," lived in deep underwater caves.
I checked the Chicago Manual of Style, but can't see this usage of quotation marks used in their examples. Which way is correct?