You may keep normal chat in all your tabs, but I definitely don't...people who don't want white text in all their tabs will hide normal from their tabs.
Yes It makes sense for it to be in green (whether you choose to make this a separate whisper tab is already up to the user - yay!)
Is it important? Probably not, but it's annoying, and theoretically should/might be a quick fix =)
EDIT- btw, thanks to the mod/person/emlee who updated my title! cheers :)