Once upon a time, web design and SEO used to be one discipline. They essentially grew out of the same place and, even now, the two skillsets are intrinsically linked.
After all, you can’t be optimising websites for SEO without those websites being built first. And you can’t be building websites with no concern for how they will perform once they’ve been set live (or you shouldn’t be, anyway).
And that’s still as true now as it ever was. So, in answer to the question ‘does my web designer need to understand SEO?’, the answer is, most definitely, yes. Of course they do. It’s blinking obvious that they need to!