I ran into the same problem, here is what I did... I noticed the added class names, esriSimpleSliderIncrementButton and esriSimpleSliderDecrementButton by the widget, but alas no id attribute. Note, this example only shows the requires I used for the tooltips. There may be an easier way, I am very new to dojo, but it works.
require(["dojo/dom-attr","dojo/query"], function(domAttr,djQuery){
navToolbar = new Navigation(map);
// I put this after I initialized the toolbar
var zoomInDiv = djQuery(".esriSimpleSliderIncrementButton");
domAttr.set(zoomInDiv[0],"title","Zoom in");
var zoomOutDiv = djQuery(".esriSimpleSliderDecrementButton");
domAttr.set(zoomOutDiv[0],"title","Zoom out");
});