I think multicol just flushes out the partly written line; it wouldn't move to a new line unless the line it's on had been partly written already, as it is here.
I tested things out, and it seems to work just fine to put the \section command inside the multicol environment (at least as well as it would be if you had a single column list there):
Code: Select all
\begin{multicols}{2}
\section{TITLE}
\begin{itemize}
\item First Item
\item Second Item
\item Third Item
\item Fourth Item
\end{itemize}
\end{multicols}
If there's something strange about that, my next suggestion was going to be to use some negative vertical space, but for some odd reason, it seemed to work just to use 0 vertical space, which is very confusing to me:
Code: Select all
\section{TITLE}
\vspace{0pt}
\begin{multicols}{2}
\begin{itemize}
\item First Item
\item Second Item
\item Third Item
\item Fourth Item
\end{itemize}
\end{multicols}
That vspace command shouldn't do anything at all, yet in that document class somehow it does. Feeling a bit to lazy at the moment to try to figure out what's going on there.