As you've discovered, different browsers often have different rules for when they choose to display certain functionality. Since these are defined by the browser, individual services like Tableau can't force the browser to render something in opposition with how it has been defined by the browser in question (such as when scroll bars appear). It's probably best to design for the more restrictive display limitation. In this case, you probably want to set your parameter height to 30 pixels to always guarantee that they scroll bars won't render.
Hope that helps,