Short answer: AUCTeX doesn't play very well with
latexmk, by default.
Long answer: AUCTeX has its own system to decide what command to run next, when building a document. This is based on reading the output of compilation program, but it expects only one command has been actually run. Instead,
latexmk runs multiple commands in a row, making AUCTeX confused. That's why the short answer.
One solution could be to write a parser specific to
latexmk, but this isn't super-easy.
However, note that AUCTeX is capable of automatically running all commands needed to build a document. Just issue C-c C-a and you're done (the output document will also be shown automatically). See also the manual. In order for this to work,
"LaTeX" should be the default command to be run, not the custom entry you added for
latexmk. The existence of this feature of AUCTeX is the reason why no one ever had the need to write the parser to make
latexmk play nicer with AUCTeX