It looks like you're using better chat? If so, you need open the WarMode.json config and in the section for BetterChat you need to add the color tag the the ModeTitleFormat property. Like this:
The Chat Color property in the mode settings of the admin panel is only for when a mode name appears in a localized message. Is it confusing? - Yes. Would it be really nice if that auto applied to BetterChat? - Absolutely. However, there are a more things you can do with BetterChat than just color the mode name, so I didnt want to hinder that customization by trying to enforce the color in addition to the other things you might customize.
Hope that makes sense? And I'm sorry for the confusing configuration.