Initially the gadget used Page Preview's classes to show tooltip and later changed to its own copies of them. However, after that, there were some visual changes to Page Preview's classes including changing border colors which didn't reflect on reference tooltips.
I hope these changes will be applyed to reference tooltips. Thanks!
I was too lazy to take on this for 3 years (hehe), but now I'm wondering does it make sense to try and match Page Previews since Reference Previews are best suited for this job. Page/Reference Previews currently use some styles that divert from Codex (including border styles you mentioned and box-shadow). I'm leaning towards updating this to Codex styles inasmuch as reasonable.