I have the sense that others on this site would disagree but, personally, I wouldn't worry about it. I don't budget, and while I do use Mint I don't pay much attention to the budget side of it. Personally, one of the great benefits of living frugally / below one's means, is NOT having to count every nickel and dime. It sounds like your SO is already doing OK.
That being said, I'd certainly share you're increased interest in FIRE with them, talk about shared goals, etc., which could motivate them to look at their spending themselves.