\documentclass[varwidth]{standalone}

\begin{filecontents}[overwrite,noheader]{test.csv}
cell1.1,cell1.2,"cell1.3.1,cell1.3.2,cell1.3.3",cell1.4
cell2.1,cell2.2,"cell2.3.1,cell2.3.2,cell2.3.3",cell2.4
\end{filecontents}

\usepackage{datatool}

\DTLread[
	name={test},
	format=csv,
	separator={,},
	delimiter={"},
	csv-content=tex,
	noheader,
	keys={first,second,third,fourth}
]{test.csv}%

\begin{document}

\DTLforeach*{test}{\first=first,\second=second,\third=third,\fourth=fourth}{%
	\first; \second; \third; \fourth \\
}

\end{document}
