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 ...
bontable*\begin{table*}[bp]– David Carlisle Dec 26 '18 at 11:55apa6class, which is notorious for its low standards of typesetting? If you've been ordered to use it, I see no reason for trying to modify the output. – egreg Dec 26 '18 at 22:29