For me (MikTeX 2.9/pdfTeX, Version 3.1415926-2.5-1.40.14) the following command fails
\tikzexternalize[prefix=../tikzcach]
with message
! Package tikz Error: Sorry, the system call 'pdflatex -shell-escape -halt-on-error -interaction=batchmode -jobname "../tikzcach/test1" "\def\tikzexternalrealjob{ch1}\input{ch1}"' did NOT result in a usable output file '../tikzcach/test1' (expected one of .pdf:.jpg:.jpeg:.png:).
I fear this is not a software defect, but a security issue in MikTeX. MikTeX simply forbids write actions on higher directory levels from what I know. I suppose that there are suitable command line options which allow it.
related: https://tex.stackexchange.com/questions/262625/security-latex-injection-hack
or https://sourceforge.net/p/miktex/discussion/33790/thread/8f4123b8/
closing ticket as this is no defect of the external library