Note that style changes apply to all tooltips on the page. Dojo creates (if necessary) 1 common dijit._MasterTooltip object containing domtip vertices, and all tooltips use it. The following code adds custom css classes to the container and the rooltips connector.
if(!dijit._masterTT)
dijit._masterTT = new dijit._MasterTooltip();
if(dijit._masterTT.domNode.childNodes[0])
dojo.addClass(dijit._masterTT.domNode.childNodes[0], "classContainer");
if(dijit._masterTT.domNode.childNodes[1])
dojo.addClass(dijit._masterTT.domNode.childNodes[1], "classConnector");
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