putting (aux log out toc bbl bib blg) files in another directory with latexmk

auxdir is the directory for all auxiliary files but not the PDF file.

latexmk -auxdir=/tmp test.tex should work. You can extend this to autocompile with latexmk -auxdir=/tmp -pdf -pvc test.tex

The manual man latexmk / texdoc latexmk explains more about the auxdir parameter:

-auxdir=FOO or -aux-directory=FOO

          Sets the directory for  auxiliary  output  files  of  (pdf)latex
          (.aux,  .log  etc).  This achieves its effect by the -aux-direc‐
          tory option of (pdf)latex, which currently is  only  implemented
          on the MiKTeX version of (pdf)latex.

          See   also   the   -outdir/-output-directory  options,  and  the
          $aux_dir,  $out_dir,  and  $search_path_separator  configuration
          variables  of  latexmk.  In particular, see the documentation of
          $out_dir for some complications  on  what  directory  names  are
          suitable.

The auxdir parameter was introduced in version 4.39.

I suppose that latexmk also can handle the option output-directory=...