Cite references in figure caption

The macro \citeA is "fragile", in the LaTeX-specific sense of the word. If it occurs inside a "moving argument" (more LaTeX jargon, sorry), such as the argument of a \caption instruction, one must prefix a \protect instruction:

\caption{\label{fig:researchscope}The process of concept-driven design approach in
    relation to theory and use situation, adopted from \protect\citeA[p.~282]{rub14}}

For another example of this type, see the posting Using \input{} inside caption.

There is a similar question in StackOverflow.

The problem with the \cite command in the figure caption is that it generates conflicts with the automatic creation of the List of Figures. So the first option is to put an alternative caption into brackets:

\caption[test caption]{test caption from~\cite{MyCite}}

You can also use the \protect environnement as suggested in the comments:

\caption{test caption from~\protect\cite{MyCite}}

As for your minimal working example, you could do it as follows:

\documentclass{book}
  \usepackage[utf8]{inputenc}
  \usepackage[pdftex]{graphicx}
  \usepackage{epstopdf}
  \graphicspath{{figures/}}

  \usepackage{lipsum} % just for the example

  \usepackage{apacite}
  \bibliographystyle{apacite}

  \usepackage{filecontents}
  \begin{filecontents}{\jobname.bib}
  @article{rub14,
     author = {Rubin, Jared},
     title = {Printing and {Protestants}: An empirical test of the role of printing in the {Reformation}},
     journal = {Review of Economics and Statistics},
     volume = {96},
     number = {2},
     pages = {270--286},
     year = {2014},
  }
  \end{filecontents}

  \begin{document}
    \listoffigures

    \vspace{0.5cm}
    \lipsum[3]
    \begin{figure}[htp]
      \centering
      \includegraphics[width=8cm,height=5cm]{sample_pic}%
      %\includegraphics[width=\textwidth]{conceptdriven.eps}
      \caption[The process of concept-driven design approach in relation to theory and use situation]{The process of concept-driven design approach in relation to theory and use situation, adopted from~\citeA[p.~282} 
      \label{fig:researchscope}
    \end{figure}

    \lipsum[2]
    \bibliography{\jobname}

   \end{document}

And the output would look like: