Add a \clearpage (or \cleardoublepage) command after \printacronyms; otherwise, the \pagenumbering{arabic} will take effect too soon. Also
As Speravir mentions in his comment, why do you include the entry for the list asKOMA classes scrbook and scrreprt offer \addchap, (and a section? I changed thatstarred version \addchap*) which can produce unnumbered chapters which show up in the table of contents and in the running heading (the starred version doesn't show up in the headings), so thet it is included as a chapterinstead of
\chapter*{List of Acronyms}
\addcontentsline{toc}{chapter}{List of Acronyms}
you can simply use, for example,
\addchap{List of Acronyms}
The code:
\documentclass[
bibliography=totoc,
headings=big,
captions=tableheading,
chapterprefix=true% like in standard class "report"
]{scrreprt}
\usepackage[left=2cm,right=2cm,top=2.5cm,bottom=3cm]{geometry}
\usepackage{xcolor}
\usepackage{graphicx}
\usepackage{minitoc}
\usepackage{setspace}
\usepackage{lmodern}
\usepackage{notoccite}
\usepackage{acro}
\usepackage{hyperref}
\setcounter{secnumdepth}{3} % number subsubsections
\setcounter{tocdepth}{3} % list subsubsections
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ACRONYM DEFINITION
\DeclareAcronym{pwr}{
short = PWR ,
short-plural = s ,
long = Pressurised Water Reactor ,
long-plural = s ,
class = reactors ,
}
\begin{document}
\pagenumbering{roman}
\cleardoublepage %<- seems not necessary
\dominitoc
\pdfbookmark[1]{Contents}{}
\tableofcontents
\cleardoublepage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LIST OF ACRONYMS
\chapter*%\chapter*{List of Acronyms}
\addcontentsline%\addcontentsline{toc}{chapter}{List of Acronyms}
\addchap{List of Acronyms}
\printacronyms[include-classes=reactors,name=Reactor Acronyms]
\clearpage
\pagestyle{headings}
\pagenumbering{arabic}
%%%%%%%%%%%%%% Chapter Style Controls
\addtokomafont{chapterprefix}{\raggedleft \linespread{1}}
\addtokomafont{chapter}{\fontsize{35}{30}\selectfont}
\addtokomafont{section}{\fontsize{20}{11}\selectfont}
\addtokomafont{subsection}{\fontsize{18}{11}\selectfont}
\addtokomafont{subsubsection}{\fontsize{16}{11}\selectfont}
\renewcommand*{\chapterformat}{%
\mbox{\scalebox{0.80}{\chapappifchapterprefix{\nobreakspace}}%
\scalebox{2.5}{\color{gray}\thechapter\autodot}\enskip}}
\chapter{Testing}
Pasting an acronym \ac{pwr}
\end{document}
Section 7.3. Options Regarding the List of the package decumentation has some explanations regarding options and customization of the list.