\raggedright behavior with minipage and tabbing

A minipage or parbox results to have the width of an inner tabbing environment only if that tabbing is the only thing inside the minipage.

So in your example

\begin{minipage}{\textwidth}
  \textbf{-added text-}
  \begin{tabbing}
    \hspace{2cm} \= \hspace{5cm} \kill
    AAAA: \> test\\
    BBBBBBBB: \> test\\
  \end{tabbing}
\end{minipage}

The width of the minipage will be \textwidth. If instead you say

\begin{minipage}{\textwidth}
  \begin{tabbing}
    \textbf{-added text-}
    \hspace{2cm} \= \hspace{5cm} \kill
    AAAA: \> test\\
    BBBBBBBB: \> test\\
  \end{tabbing}
\end{minipage}

then the result will be what you want (possibly with space missing). You can use the varwidth environment of the package with the same name:

\documentclass{article}
\usepackage{varwidth}
\begin{document}

\begin{center}
Example of text just to see that the centering will be correct

\begin{varwidth}{\textwidth}
  \textbf{-added text-}
  \begin{tabbing}
    \hspace{2cm} \= \hspace{5cm} \kill
    AAAA: \> test\\
    BBBBBBBB: \> test\\
  \end{tabbing}
\end{varwidth}
\end{center}
\end{document}