The main wrapper of the tooltip is animated and the callout is positioned and shown after that. This makes it "pop" after the animation finishes. Disabling the shadow (EnableShadow=false) mitigates the effect somewhat.
The callout can be positioned initially (if ShowCallout is not set to false) where it should be according to the Position property of the RadToolTip and its location can be updated at the end of the entire showing process again (as it is now).