Oh. I have seen this behaviour in other programs, recently mostly in Cisco AnyConnect. I always thought this an OS glitch.
- show the tooltip - rely on move events on the main window to hide it
the move events are usually received only when the window is visible (and focused depending on the os), unless you take extra measures to grab the pointer and/or listen on global events, which involves more trickery to work right.
It's the classic scenario where a decent system toolkit has this figured out and solved for you, while doing the same by hand looks somewhat easy and normally works 95% of the time, but fails in odd ways and drives your power users crazy.
Driving UIs heavily by keyboard and shortcut is the sure-way to hit that remaining 5% all the damn time nowdays...