Color correcting is a whole can of worms, but it really does help to conceal the dark purple areas under my eyes.
To cancel out the purple, I usually start my under-eye routine by using a peach- or orange-based concealer or color corrector. It's just one step of many.
Lately I've been using and loving Make Up For Ever Ultra HD Invisible Cover Concealer, which has an orange tint.
Now, if you're in your 40s like I am, or really any age, and you have any fine lines, things can start to look bad under your eyes the moment you get too much product down there. It can look thick and heavy. I see YouTubers do this all the time -- put a ton of concealer and the whole kitchen sink under their eyes. If you don't want your under-eye area looking cakey, it isn't usually a good idea, so I put a small amount of the product on the back of my hand, and then I pick up just the littlest amount with my finger.