Here's one attempt, where I've added some conditional code to add the leading zero if the number is less than 10. The idea is like this (for the minutes part):
\pgfmathparse{ifthenelse(\minutes<10,0,)}\pgfmathresult\pgfmathprintnumber{\minutes}:%The \pgfmathparse will store either 0 or an empty string depending on whether a leading zero is required (determined by testing if \minutes is less than 10). This is then dumped into the \def of the top-level \pgfmathresult by invoking \pgfmathresult inside the group, which is followed by the \pgfmathprintnumber for the number of minutes itself.
Unfortunately I was not really able to solve the 12:60 rounding issue. I thought maybe defining \seconds, \minutes, and \hours from the bottom up rather than the top down would help, but that caused issues elsewhere.
But: disabling the FPU makes it correct with no detrimental effects, because pgfplots does its own scaling to avoid "Dimension too large" errors. So it may or may not be an acceptable solution for you.
I also changed the options for the printing of \seconds:
\pgfmathprintnumber[fixed,fixed zerofill]{\seconds}%Adding fixed"locks in" fixed mode so scientific notation is never used, and the fixed zerofill will always be respected (since we're always in fixed mode).
\documentclass{article}\usepackage{pgfplots}\pgfplotsset{compat=1.12}\usepgfplotslibrary{dateplot}\def\transformtime#1:#2:#3!{% \pgfkeys{/pgf/fpu=true,/pgf/fpu/output format=fixed} \pgfmathparse{#1*3600-\pgfkeysvalueof{/pgfplots/timeplot zero}*3600+#2*60+#3}% \pgfkeys{/pgf/fpu=false}}\pgfplotsset{ timeplot zero/.initial=0, timeplot/.style={ y coord trafo/.code={\expandafter\transformtime##1!}, y coord inv trafo/.code={%% \pgfkeys{/pgf/fpu=true,/pgf/fpu/output format=fixed,} \pgfmathsetmacro\hours{floor(##1/3600)+\pgfkeysvalueof{/pgfplots/timeplot zero}} \pgfmathsetmacro\minutes{floor((##1-(\hours - \pgfkeysvalueof{/pgfplots/timeplot zero})*3600)/60)} \pgfmathsetmacro\seconds{##1-floor((##1)/60)*60} \def\pgfmathresult{% \pgfmathparse{ifthenelse( \hours<10,0,)}\pgfmathresult\pgfmathprintnumber{\hours}:% \pgfmathparse{ifthenelse(\minutes<10,0,)}\pgfmathresult\pgfmathprintnumber{\minutes}:% \pgfmathparse{ifthenelse(\seconds<10,0,)}\pgfmathresult\pgfmathprintnumber[fixed,fixed zerofill]{\seconds}% }% \pgfkeys{/pgf/fpu=false} }, scaled y ticks=false, yticklabel=\tick }}\begin{document}\begin{tikzpicture}\begin{axis}[ timeplot, timeplot zero=0, ytick={00:11:30.056, 00:12:00, 00:13:00, 00:14:00},]\addplot table {State Time -13 00:12:42.40-12 00:12:57.06-11 00:13:17.59-10 00:13:40.83-9 00:14:07.44-8 00:14:31.11-7 00:14:04.28-6 00:14:12.07-5 00:14:09.27-4 00:13:59.92-3 00:13:56.82-2 00:13:55.17-1 00:13:53.520 00:13:52.471 00:13:59.322 00:14:00.583 00:13:43.124 00:13:49.055 00:13:28.637 00:11:15.6256432};\end{axis}\end{tikzpicture}\end{document}