Hi,
Setting a custom css class to tooltip container can be done:
1. Using reference on widget popup
var
widget = $(
'#tooltip'
).kendoTooltip().data(
'kendoTooltip'
);
widget.show();
widget.popup.element.addClass(
'CUSTOM_CLASS'
);
Using this approach you will be content that all necessary logic of showing tooltip executed and you can manipulate with this element css as you want.
2. Create your own widget extended from kendo.ui.Tooltip. In this case you can manipulate with tooltip as you want.
Information how to create custom widget you will find here