The simplest way to solve this issue is to destroy all the tooltip when start dragging a node and then restore all the tooltip when stop dragging.
<ul class="easyui-tree" data-options="
data:data,animate:true,dnd:true,
formatter:function(node){
return '<span title=\'' + node.text + '\' class=\'easyui-tooltip\'>' + node.text + '</span>';
},
onStartDrag:function(node){
$(this).find('.tooltip-f').tooltip('destroy');
},
onStopDrag:function(node){
$.parser.parse($(this));
},
onLoadSuccess:function(){
$.parser.parse($(this));
}"></ul>