Are you seeing the same thing in one of the WP default themes? That looks like a CSS issue within your theme. You’ll need to use a web inspector (like Firebug or the Inspect Element option in browsers) to sort out what the offending CSS code is. By default I don’t see any hover actions in Twenty Thirteen.
The BuddyPress Plugin doesn’t apply any style when you hover over a suggested @mention. When using a default WP theme (which is what the BP developers base their testing on) there is no hover effect on the suggested username. Which indicates that it is probably something in the style of the theme you are using that is applying this additional effect.
The quickest way to see if it’s the theme or not, is to quickly change themes to one of the Twenty-xx themes that are packaged with WordPress, and if the hover effect disappears, you know where the problem is.
That’s only part one. The next part is to figure out where in the theme the issue is and patch it.