I don't see a CSS class that is referenced by the guides for things you already call relating to the styling of the popup boxes when hovering over items like recruiting links.

I would like to be able to set the background color, text color, and add padding to this.

The recruiting menu currently uses some non-classed popup. I'll have to update it to use the more usefil transtooltip() call I've been using.

For those type of popups, you can override the default with a .transtooltip {} css rule, though you'll have to use a few !importants to make it work.