Is this cleaning my hair??!!!

So after before getting in the shower I applied one of my HG products to my scalp to get it extra clean. It's called ELLiN LAVAR Scalp RX. I suffer from atopic dermatitis and dry scalp but this has caused my scalp to heal immensely. As I was scrunching my hair, it dawned on me...was this actually cleaning my hair? It had many anti-fungicides in it, but it also contained nourishing oils as well. In fact here is the ingredient list:

SD Alcohol 40B; Water; Propylene Glycol; Salicylic Acid; Aloe Barbadensis Leaf Juice; Passiflora Edulis Seed Oil; Passiflora Incarnata Seed Oil; Caryocar Brasiliense Fruit Oil; Vitis Vinifera (Grape) Seed Oil; Bertholletia Excelsa Nut Oil; Theobroma Grandiflorum Seed Butter; Hydrolyzed Wheat Protein; Parfum; Menthol; Benzophenone-4; Tocopheryl Acetate; Melaleuca Alternifolia (Tea Tree) Oil

I know that it cleans my scalp, but because I comb it through I was wondering if it also cleaned my hair. Regardless, I encourage EVERYONE who suffers from dry scalp or dandruff to invest in this product!