The issue is that you are declaring an initial basemap when you create the map. I've commented out that line, and added your code to add your tiled service.
<script>
var map;
require([
"esri/map", "esri/InfoTemplate",
"esri/layers/FeatureLayer", "esri/dijit/HistogramTimeSlider",
"dojo/parser", "dojo/dom-construct",
"dijit/layout/BorderContainer", "dijit/layout/ContentPane",
"dojo/domReady!"
], function(
Map, InfoTemplate,
FeatureLayer, HistogramTimeSlider,
parser, domConstruct
) {
parser.parse();
map = new Map("mapDiv", {
basemap: "streets",
center: [-37.32, 33.22],
zoom: 4
});