You've already run the experiment and reported the result: tight and shiny at the same time is oily-but-dehydrated skin, and it's exactly what skipping moisturizer produces for a lot of oil-prone people. Oil (sebum) and water content are different systems — your glands can pump out plenty of oil while the skin itself is short on water. Moisturizer manages the water side.
The fix isn't slathering a heavy cream; it's picking the right texture. What your skin wants is a humectant-forward, lightweight formula: gel or gel-cream, built on ingredients like glycerin or hyaluronic acid that pull water into the skin, with just enough emollient to keep it there (how humectants and occlusives divide the labor: https://www.ncbi.nlm.nih.gov/books/NBK545171/). Hyaluronic acid's hydration effect is genuinely immediate — measurable after a single application (https://pmc.ncbi.nlm.nih.gov/articles/PMC8322246/) — so you'll know quickly whether the tightness resolves. Niacinamide is a sensible ingredient to see on the label too: it supports the barrier's own lipid production and is well tolerated daily (https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1365-2133.2000.03705.x).
One texture note: if a product leaves you shinier, that's the formula, not proof that moisturizing is wrong for you — gel formulas exist precisely for this. And if you're using oil-control actives like salicylic acid or benzoyl peroxide, moisturizer is what keeps them sustainable; dehydrated, irritated skin tolerates actives badly.
So yes: cleanse gently, moisturize light, SPF in the morning. Your 10am face is telling you about your sebum, not vetoing hydration.