This is the expected behavior, the ToolTipManager has otherwise no way of knowing how big it should be. It is a complex HTML structure and without any explicit dimensions the size falls back to the default dimensions of the HTML elements, which are usually simply the borders.
I would also advise that you set the ShowEvent property to the desired value, as otherwise some unexpected behavior may be observed.
Generally speaking, all the layout and behavior properties need to be set explicitly in order for it to work properly. These include Position, RelativeTo, ShowEvent, HideEvent, Width, Height, target controls/autotooltipify (used best with tooltipify zone). For the RadToolTip the IsClientID property is as important as the TargetControlID property, too.
the Telerik team
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