There should be a method like GetRadWindowManager for RadToolTipManager called GetRadToolTipManager. This could be under the static $telerik.static library or as a global function that can be directly called without any prefixes.

The goal is to find the RadToolTipManager in an easy and transparent manner in any content page, otherwise one needs to get the id from master page and then use $find, which is not an easy and transparent way of getting the manager object.

At present, when content arrives from one of the load-on-demand mechanisms in RadToolTipManager (AJAX request, web service, WCF web service), it is expected that it has static dimensions that match those set in the Width and Height property of the control.

Having an autosizing feature similar to RadWindow's should let it update its size (e.g., height by provided width) and position according to the new content when it arrives.

Samples are attached that showscase examples of resizing the tooltip once content arrives so you can use as base and implement similar resizing logic by calculating the dimensions of the content that came back.

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).