The RadToolTip is actually positioned absolutely. You can confirm this by inspecting its popup with your developer tools of choice. This means that resizing the browser would, generally, not affect its position even though it can affect elements with static position.
What you can do is to call the updateLocation() method of the currently active tooltip when the window resize is done. How to get a reference to the currently shown tooltip is shown here
(see the getCurrent static method) and this SO thread
may be useful on handing the window.resize event.
I also advise that you examine the Common Issues help article and make sure your tooltips cover the guidelines there - they have Width, Height, RelativeTo set. I also advise that you set their RenderInPageRoot property to true.
I am attaching here a simple page that shows this in action together with a video that shows the behavior.
the Telerik team
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