Why does my oily skin still feel tight or dry?

Oil production and hydration are two separate things — skin can be oily and dehydrated at the same time, especially if you're over-cleansing.

Oiliness is about how much sebum your skin produces; hydration is about how much water is in the skin. It's entirely possible to have both an overactive oil gland and a water-depleted surface — usually from stripping cleansers, skipping moisturiser because "oily skin doesn't need it," or over-exfoliating. The skin responds to that dehydration by producing even more oil, which reads as "oily and tight" at the same time.