You do need to let the dandruff shampoo sit in your hair and on your scalp for a couple of minutes before rinsing it out.
Allowing the dandruff shampoo to sit on your scalp and in your hair for a few minutes allows the active ingredients in the dandruff shampoo to work on the scalp effectively to loosen the dandruff flakes.
Most of the dandruff shampoos also recommend that you leave the dandruff shampoo on your scalp and hair for 3 minutes to 5 minutes.
Then after you allow the dandruff shampoo to sit for a few minutes or so you can then rinse it out.
The active ingredients in the dandruff shampoo target the root cause of the dandruff, like fungal overgrowth or excessive shedding of skin cells.
Leaving the dandruff shampoo in your hair and on your scalp for a few minutes allows the active ingredients in the dandruff shampoo to penetrate your scalp and address the underlying cause of the dandruff.
After you do allow the dandruff shampoo to sit, you can then thoroughly rinse the dandruff shampoo from your hair as well as your scalp to remove any loosened dandruff flakes and shampoo residue.
It's also good to follow up with a moisturizing hair conditioner after you use the dandruff shampoo, which can keep your hair moisturized as dandruff shampoo can sometimes dry out your hair.
Also while you're waiting and allowing the dandruff shampoo to work on your hair you should gently massage your scalp to help loosen the dandruff flakes and also improve circulation.