In the documentation, the explanation of /tikz/cm says that the transformation is
$ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} t_x \\ t_y \end{pmatrix} $
but actualy b and c are interchanged, the real transformation is
$ \begin{pmatrix} a & c \\ b & d \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} t_x \\ t_y \end{pmatrix} $
By the way, there is another misspelling too :
/tikz/pic action
should be replaced by
/tikz/pic actions
(with s at the end) as shown in the example after the key.
I confirm the mistake in the cm dokumentation and fixed both issues in the documentation.
Thanks for the report.
I haven't seen the bug #304 when I posted this one. I think it is the same bug.
Last edit: Kpym 2015-08-08