Well I found the solution to the problem here. Quoting from the post there:
Alright, I solved it. Something about upgrading to OSX Mavericks
changed the path in which the MacTeX TeXLive distribution was located.
...I had to go into LaTeXTools.sublime-settings and change the OSX path. The default
setting for OSX is:
"texpath" : "$PATH:/usr/texbin:/usr/local/bin:/opt/local/bin"
You just have to add the following path (/usr/local/texlive) to get
things to work:
"texpath" :
"$PATH:/usr/texbin:/usr/local/texlive:/usr/local/bin:/opt/local/bin"
I found a solution. I have not validated beyond the fact that, by doing these things, I got it to work. It's possible there are extraneous steps, and any improvements are welcomed.
First, I made sure that my MikTex was up to date (and thus had Biber installed). Second, I installed the latexmk package using the Package Manager. Third, I added an environemntal variable BIBTEX that pointed to biber in the MikTex bin\ folder.
Then, I modified the traditionalBuilder.py file so that, the default command for MIKTEX was the same command (beginning with latexmk) as used for other engines. I realize that modifying the default builder is a very bad idea, but I was unable to get custom builders to work, even when I simply changed the builder_path to User\builder and copied traditionalBuilder.py to that folder (renaming it, of course).
After doing this, building via Sublime yielded the desired results.
I had hoped to get simpleBuilder to work, but it refused to run bibtex, despite my efforts. Ultimately, my solution works, but it's not very elegant.
Best Answer
Heads up: there is now a branch of the "official" LaTeXTools package that supports ST3. See http://tekonomist.wordpress.com for details. The code is based on phyllisstein's port but incorporates all recent fixes to the master branch.
Let me know how it works for you, and please report any issues on GitHub (there is an issue specifically for ST3 problems).
Marciano (LaTeXTools author)