/Update/ How could I make the caption of table upright?

Well, if you check the code of class apa6.cls you can find the following code:

\ifapamode{% man
    \DeclareCaptionLabelFormat{tablelabel}{\hspace{-\parindent}\raggedright#1 #2}
    \DeclareCaptionLabelFormat{figurelabel}{\hspace{-\parindent}\raggedright\textit{#1 #2}}
    \DeclareCaptionTextFormat{tabletext}{\hspace{-\parindent}\raggedright\textit{#1}}
}{% jou
    \DeclareCaptionLabelFormat{tablelabel}{\hspace{-\parindent}#1 #2}
    \DeclareCaptionLabelFormat{figurelabel}{\hspace{-\parindent}\textit{#1 #2}}
    \DeclareCaptionTextFormat{tabletext}{\hspace{-\parindent
}\textit{#1}} % <===========================================================
}{% doc
    \DeclareCaptionLabelFormat{tablelabel}{\hspace{-\parindent}#1 #2}
    \DeclareCaptionLabelFormat{figurelabel}{\hspace{-\parindent}\textit{#1 #2}}
    \DeclareCaptionTextFormat{tabletext}{\hspace{-\parindent}\textit{#1}}
}

I marked the relevant place with <=========: there it is defined that the title should be italic. To get rid of that change \textit{ to \textup{ (mentioned in comment of @mico):

ifapamode{% man
    \DeclareCaptionLabelFormat{tablelabel}{\hspace{-\parindent}\raggedright#1 #2}
    \DeclareCaptionLabelFormat{figurelabel}{\hspace{-\parindent}\raggedright\textit{#1 #2}}
    \DeclareCaptionTextFormat{tabletext}{\hspace{-\parindent}\raggedright\textit{#1}}
}{% jou
    \DeclareCaptionLabelFormat{tablelabel}{\hspace{-\parindent}#1 #2}
    \DeclareCaptionLabelFormat{figurelabel}{\hspace{-\parindent}\textit{#1 #2}}
    \DeclareCaptionTextFormat{tabletext}{\hspace{-\parindent
}\textup{#1}} % <================================================================
}{% doc
    \DeclareCaptionLabelFormat{tablelabel}{\hspace{-\parindent}#1 #2}
    \DeclareCaptionLabelFormat{figurelabel}{\hspace{-\parindent}\textit{#1 #2}}
    \DeclareCaptionTextFormat{tabletext}{\hspace{-\parindent}\textit{#1}}
}

With the following complete code

\documentclass{apa6} % 

\ifapamode{% man
    \DeclareCaptionLabelFormat{tablelabel}{\hspace{-\parindent}\raggedright#1 #2}
    \DeclareCaptionLabelFormat{figurelabel}{\hspace{-\parindent}\raggedright\textit{#1 #2}}
    \DeclareCaptionTextFormat{tabletext}{\hspace{-\parindent}\raggedright\textit{#1}}
}{% jou
    \DeclareCaptionLabelFormat{tablelabel}{\hspace{-\parindent}#1 #2}
    \DeclareCaptionLabelFormat{figurelabel}{\hspace{-\parindent}\textit{#1 #2}}
    \DeclareCaptionTextFormat{tabletext}{\hspace{-\parindent
}\textup{#1}} % <================================================================
}{% doc
    \DeclareCaptionLabelFormat{tablelabel}{\hspace{-\parindent}#1 #2}
    \DeclareCaptionLabelFormat{figurelabel}{\hspace{-\parindent}\textit{#1 #2}}
    \DeclareCaptionTextFormat{tabletext}{\hspace{-\parindent}\textit{#1}}
}

\usepackage{multirow}

\begin{document}

\begin{table*}[bp]
\centering
 \vspace*{2em}
  \begin{threeparttable}
  \captionsetup{font=up, labelfont=bf, labelsep=newline}
  \caption[font={up}]{Behavioural performance during the perceptual judgement functional magnetic resonance imaging task}
  \label{tab:Beh}
  \begin{tabular}{*{7}{l}}  \toprule
  \multirow{2}*{} & \multicolumn{3}{l}{Young} & \multicolumn{3}{l}{Old} \\
  \cmidrule(lr){2-4}\cmidrule(lr){5-7} & Rep 1 & Rep 2 & Rep 3 & Rep 1 & Rep 2 & Rep3 \\
    \midrule
  Proportion correct & 0.90 (0.09) & 0.94 (0.07) & 0.94 (0.05) & 0.88 (0.10) & 0.90     (0.08) & 0.91 (0.09) \\ 
RT (ms) & 783 (68) & 669 (53) & 662 (81) & 938 (113) & 830 (121) & 811 (107) \\
\bottomrule
\end{tabular}
\smallskip

   \begin{tablenotes}
 {\small
        Accuracy and reaction time (RT) means (standard deviation) for stimuli presented the first time (Rep 1), second time (Rep 2), and third time (Rep 3) in the perceptual judgement task.
                 }
    \end{tablenotes}
  \end{threeparttable}
\end{table*}

\end{document}

you get the result:

But be warned: Do not change the style of apa6 like this if you have to submit a paper. The journal then wants the title to be in italic letters ...

• The default behavior is upright text in the caption of a table afaik.
• I attached a small example to show what I mean.
• I assume that somewhere in your preamble there is the package caption included.
• Do you see something like textfont = it in your preamble as an option to the caption-package?
• Update: In your code, I see \captionsetup{font=up, labelfont=bf, labelsep=newline}, so I assume you are aware of the caption package. Without further information from your side, it's hard to help.

---

\documentclass{article}
\usepackage{threeparttable}

\begin{document}

% Example taken from https://tex.stackexchange.com/questions/118743 and modified
\begin{table}
\caption{Some very informative caption}
\begin{threeparttable}
\begin{tabular}{lll}
TextText\tnote{1} & TextText & TextText \\ 
TextText & TextText\tnote{2} & TextText \\ 
\end{tabular}
\begin{tablenotes}
\item[1] Some remark. \item[2] Another remark.
\end{tablenotes}
\end{threeparttable}
\end{table}

\end{document}

---

Unrelated, maybe make yourself familiar with the "rules" around here, e. g. https://stackoverflow.com/help/how-to-ask and I've just been asked to write a minimal example, what is that?.

As pointed out in this answer, the apa6 document class automatically loads the caption package and the format of the text part of a table-related caption is set via the directive

\DeclareCaptionTextFormat{tabletext}{\hspace{-\parindent}\textit{#1}}

To redefine this, simply run

\DeclareCaptionTextFormat{tabletext}{\textup{#1}}

in your preamble.

Aside: As @egreg has noted in a separate comment, the quality of the LaTeX code in the file apa6.cls is not exactly great. To wit, the directive \hspace{-\parindent} in the original form of \DeclareCaptionTextFormat does nothing useful because the \parindent length parameter is set to 0 inside table and figure environments automatically; hence, \hspace{-\parindent} does nothing and should be omitted.