tooltips: It is possible more places need a "sanity check" to clear possible artifacts that remain on screen. That said, lingering tooltips do not have anything to do with the boffing mini-game at all. Various tooltips are created generally from moving the mouse across the border (from outside to inside) of items that have tooltips set on them. These same tooltips are then hidden when the mouse moves across a border in the reverse direction of that same item or any other that shares the same tooltip feature. There are ways to manipulate software such that the mouse never actually crosses the boundary in the reverse direction such that it can be detected (especially if using keyboard shortcuts to launch new screens). All of this is generally not a problem until the player navigates to an entirely new screen when there is no usage of that same tooltip style and thus no boundary to cross to make it go away.
Long story short, the tooltip is almost certainly already on the screen (somewhat in error). And then you are clicking and going into the boffing scene. While it isn't a fix, you can pay closer attention to when tooltips are present when you do not desire them to be and move the mouse appropriately to close them prior to advancing on to a different environment (as a workaround until more sanity checks are in place).
But mentioning how you went about launching the boffing game without the tooltip already being turned off would be useful information.
Really though, the names of chars in the boffing area should be changed to have the char tooltip anyway (which would give the player a way to turn it off).