I have a variety of cleansers, including Clarins. I totally ignore the "instructions", which I agree are often "precious" nonsense! I massage them in, and I use a flannel and warm water to remove every single one of them, then tone, usually with Liz Earle Instant Boost Skin Tonic. I've never had a problem with not getting makeup off or having any residue... And I never use cotton wool pads for either cleansing or toning. My only exception to washing off the cleanser is when I've got very little time, and I use the micellar water (the B. Pure one from Superdrug) - that I put on cotton wool pads and swipe all over face, neck and decolletage.
I go for enough facials to know that while they use the dreaded tissue to pat off the residue of the toner, they don't apply the toner on cotton wool pads, so neither do I (it's a waste of money going into the cotton wool pad, not onto your face).
Emma Hardie and Elemis cleansing balms are my favourite though - very effective, great for massage, smell divine and leave my skin silky soft. I know not everyone can, but I use them round my eyes as well with no ill-effects.