The tightness you feel is damage, not cleanliness
That squeaky-clean feeling after washing your face is your skin's acid mantle in distress. The acid mantle is a thin, slightly acidic film, pH between 4.5 and 5.5, that sits on the surface of healthy skin and keeps bacteria out and moisture in. When a cleanser strips it away, nerve endings register the absence of sebum and send a tightness signal. That signal is not cleanliness. It is your barrier telling you it has been compromised.