How to position text on top of a node?

The minipage environment has a couple of optional arguments:

• [pos] takes one of t, b, c, which will position the minipage at the top, bottom or center of the surrounding text line, respectively
• [height] specifies the height of the minipage
• [inner pos] again takes one of t,b,c, but this time it specifies the position of the content inside the minipage

In your case, you could use

\begin{minipage}[t][5cm]{5cm} ... \end{minipage}

to position the text. Your node will then have a width and height of 5cm + 2*inner sep.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning}
\begin{document}
\tikzset{every node/.style={rounded corners}}
\begin{tikzpicture}
\node[draw,fill=yellow] (n1) {
    \begin{minipage}[t][5cm]{5cm}
        alignment of nodes

        with \verb|minipage|

        long text

        fourth line
    \end{minipage}
};

\end{tikzpicture}

\end{document}

Jake's answer is good, but if you really want to obey the minimum height, i.e. allow the nodes also to be larger you would need to measure the height (actually the depth) by yourself and increase it if required. You can code an own environment for this which takes the width and totalheight as two arguments.

The height argument can also be replaced by reading out the minimum height argument using \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/minimum height}}%.

\documentclass{report}

\usepackage{tikz}
\usetikzlibrary{positioning}

\makeatletter
\newenvironment{minsizebox}[2]{%
    \pgfmathsetlength\@tempdima{#2}%
    \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/inner ysep}}%
    \advance\@tempdima by -2\pgf@yc
    \begin{lrbox}{\@tempboxa}%
        \begin{minipage}[t]{#1}%
           \vspace{0pt}%
}{%
        \end{minipage}%
    \end{lrbox}%
    \ifdim\@tempdima>\dp\@tempboxa
        \dp\@tempboxa=\@tempdima
    \fi
    \box\@tempboxa
}
\makeatother

\begin{document}

\tikzset{every node/.style={rounded corners,minimum height=5cm}}
\begin{tikzpicture}
\node[draw,fill=yellow] (n1) {%
    \begin{minsizebox}{5cm}{5cm}
        alignment of nodes

        with \verb|minipage|

        long text

        fourth line
    \end{minsizebox}%
};
\end{tikzpicture}
\begin{tikzpicture}
\node[draw,fill=yellow] (n1) {%
    \begin{minsizebox}{5cm}{5cm}
        alignment of nodes

        with \verb|minipage|

        long text

        long text

        long text

        long text

        long text

        long text

        long text

    \end{minsizebox}%
};
\end{tikzpicture}
\begin{tikzpicture}
\node[draw,fill=yellow] (n1) {%
    \begin{minsizebox}{5cm}{5cm}
        alignment of nodes

        with \verb|minipage|

        long text

        long text

        long text

        long text

        long text

        long text

        long text

        long text

        long text

        long text

        long text

        long text

        long text

        long text

        long text

        long text

    \end{minsizebox}%
};
\end{tikzpicture}
\end{document}