The ColReorder plug-in interacts with the ColVis plug-in for DataTables by updating the order of the list of columns whenever a reorder is done. This is shown in the example below, where one column has been hidden by default to add extra emphasis to ColVis.
$(document).ready( function () {
	var oTable = $('#example').dataTable( {
		"sDom": 'RC<"clear">lfrtip',
		"aoColumnDefs": [
			{ "bVisible": false, "aTargets": [ 1 ] }
		]
	} );
} );