exists $generated_log{"$bbl_base.bcf"} does a test if the list of files %generated_log includes an entry for "$bbl_base.bcf". From my point of view such an entry is missing in the list %generated_log, the reason why the call fails. If you test it with -e which does in general the same, it works in fact of the now missing check of %generated_log. You should report it to the author. It could also be possible that some of the Perl functions have not the same behaviour as with Linux.
I've made a new version of latexmk, which supports -aux-directory and -output-directory. It's v. 4.27a and can be found at
http://www.phys.psu.edu/~collins/latexmk/versions.html
This version will be submitted to CTAN fairly soon, but some feedback would be useful, since I have not tested the new features extensively, especially as I don't have current access to MiKTeX or a more recent one can be found on CTAN as well.
Latexmk now has options -auxdir, -aux-directory, -outdir, and -out-directory, plus corresponding configuration variables $aux_dir and $out_dir. See the documentation for more details. To achieve what the original poster wanted, it's sufficient to put
$aux_dir = 'C:/Users/doncherry/Documents/LaTeX/AUXI_global';
in a latexmkrc file. (I've used forward slashes in directory names since these are acceptable to MS-Windows, and avoid running afoul of quoting conventions.)
I've done some tests with the -output-directory option, and the only problem that needs sorting out is that the combination of biblatex with bibtex doesn't work because a file needed by bibtex isn't in its usual place. (Biblatex with biber works, as do ordinary uses of bibtex.) If you don't use biblatex, the last issue doesn't affect you.
Best Answer
If you run
latexmkwith the argument-pdf, it will compile withpdflatex.In TeXWorks:
On Linux, change the `~/.latexmkrc' file as per this SE answer.