Starznthings: Tea tree oil can be effective if used in dilute form regularly on mild seborrhoeic dermatitis (UK spelling!). You may find some of the other oils and extracts in the Trader Joe's irritating tho, the tingle is a sign of mild irritation. Also the shampoo contains cwhich can be stripping/ irritating.
THE NATURAL HAVEN: Are sulfate free shampoos really gentler?
Your entire routine is relevant, aim to use super gentle products at pH 4.5 to 5.5 to respect the skin barrier/ protective acid mantle/ beneficial flora. You probably already know to cleanse regularly. Options for sulphate free shampoos include
Best Hair Loss Treatments | Hair Growth Treatment | Treatment For Hair Growth (contains ketoconazole, same as in Nizoral)
Products - Komaza Care (pH 4.5 gentle scalp friendly ingredients)
Neutrogena T/Sal Therapeutic Shampoo Ulta.com - Cosmetics, Fragrance, Salon and Beauty Gifts (salicylic acid, harsher so perhaps better for more severe SD)
Also review your diet, aim for as anti inflammatory nutrient dense as possible - over time that can make a huge difference alongside a gentle routine by altering the amount and composition of your sebum, strengthening the skin barrier, reducing systemic inflammation.