Different caption alignment on different longtable pages

You could define a couple of new commands that change the captionsetup and then pass arguments to caption. It is then possible to set a document-wide parameter, such as labelfont=bf that affects both captions.

\documentclass[12pt,a4paper]{article}

\usepackage{longtable}
\usepackage{caption}
\usepackage{booktabs}

\captionsetup[table]{singlelinecheck=false,labelfont=bf}
\newcommand\firstcaption[1]{\captionsetup{justification=raggedright}\caption{#1}}
\newcommand\followingcaption[1]{\captionsetup{justification=raggedleft,labelsep=space}\caption[]{#1}}

\begin{document}
    \listoftables%
    \clearpage%
    \renewcommand*{\arraystretch}{1}
    \begin{longtable}[t]{l}
        \firstcaption{Summary of qualitative risk factors\label{tab:label1}}\\
        \toprule
        \textbf{First Column} \\
        \midrule
        \endfirsthead

        \followingcaption{(Continue): Summary of proven determinants for falling}\\
        \toprule
        \textbf{Author} \\
        \midrule
        \endhead

        \newpage
        \bottomrule

    \end{longtable}
\end{document}

As mentioned in my comments, I would really suggest to avoid the tabu package.

Here is a sample solution with longtable and booktabs:

\documentclass[12pt,a4paper]{article}
\usepackage{longtable}
\usepackage{caption}
\usepackage{booktabs}
\usepackage{hyperref}

\captionsetup[table]{labelformat=simple,justification=raggedright,singlelinecheck=false}

\begin{document}

\renewcommand*{\arraystretch}{1}
\begin{longtable}[t]{l}
    \caption{Summary of qualitative risk factors}\label{tab:label1}\\
    \toprule
    \textbf{First Column} \\
    \midrule
    \endfirsthead
    \caption*{\raggedleft Table \ref{tab:label1} (Continue): Summary of proven determinants for falling  }\\
    \toprule
    \textbf{Author} \\
    \midrule
    \endhead

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    \bottomrule

\end{longtable}


\end{document}

As you can see, I added a couple of features I thought you might like:

1. I don't use the tabu package (see why here).

2. I'm using the booktabs package to improve the horizontal lines

3. I'm not defining new commands (you could also see this as a weakness).

4. I'm using hyperref to be able to "jump back" to the beginning of the table