Potentially part of your issue is that you use shampoo, particularly if it's really strong. Shampoo strips oil from your hair, which is why you need conditioner to add oil back. Your scalp naturally produces oil to protect your hair. If you strip it, particularly if you don't replace it, your scalp will go crazy producing oil.

Eventually going no-poo this dies down as everything normalizes. For a little while, it'll be pretty oily though. What I did many years ago is I went from washing with shampoo daily to every other day, to once or twice a week, reducing until I hit zero. Wash with water daily though. I also recommend trying conditioner washing as an alternative to transition as well. The oil in your hair will bind to the oil in the conditioner and clean your hair, but it doesn't strip it dry. That'll probably help reduce how much your scalp needs to produce.

Obviously it's your hair. Everyone is different. This may not be something that can work for you, but you can't know until you do some experiments. I wouldn't assume it's the case yet.