That is all you need to do.
Rinse throughly, shake out the excess water (no need for violence here, just give a good shake), and then set or, better still, hang it out to dry in where there's air circulation.
If you get soap buildup, then A) maybe you aren't rinsing throughly, B) question your soap; a good shaving soap rinses clean easily, and C) soak the brush in a cup of hot water with a tablespoon or two of borax (get it at the grocery where the laundry soap is sold; not being a featured product, it's usually on the bottom shelf).
You shouldn't have to do the borax soak at all, ever. And if you do need it, it should be rare and on an as-needed basis.
Really, brush care should be easy.
DE wet-shaving is something which should be easy and carefree. It should be quick and utilitarian because you do it everyday. It need not consume a lot of attention.