The vast majority of those using magic do not realize they are using magic. So the local healer who has an uncanny knack for healing wounds is unwittingly using open/closed healing related lists without actually knowing that's what they are doing. The vast majority of magic is innate talent which is self-taught in ignorance - they just know they have a 'feel' for what they are doing.
Another thing that doesn't make sense. I am assuming that there is no "Detect Magic" in your world, otherwise, long ago it would have been figured out what people are doing. My favorite series
The Wheel of Time has this exact situation in it. in the very first book,
The Eye of The World, one of the characters is the village "wise-woman" (called a Wisdom there), who is responsible for the healing of villagers, among other things. She is super good at this, able to heal people in miraculous fashion, not knowing she is channeling (magic in that series) all the while. This ignorance comes to a screeching halt when an actual Aes Sedai, a full channeler (magician for all intents and purposes), comes to the village. That is as long as ignorance lasts, right up until someone who knows shows up and is willing to say something. In a world in which 20% of the population (your number) does some form of magic, it would happen very quickly, I believe.
You seem to be applying your own settings logic to mine.
No, I am applying a "realistic" ideology to the situation; extrapolating a natural course of events given the parameters stated.
For people to continue performing magic without their knowledge requires an absence of magic detection. As that is one of the basic abilities of mages, I don't see it happening for long. Take Shadowrun as an example: magic returns, adepts start doing things but don't know what it is - for a while. Then a full mage comes along, watches them, and goes, "Hey. Do you know you are doing magic? Well, you are." [Insert, "The More You Know" PSA here.]
Take dragons in my setting for example. They exist, but they are not exactly common, are intelligent, and avoid being seen, let alone in large population centers, for the most part. I could go into way more detail, but it's all beside the point (and possible spoilers for those I play with). The point is the majority of the population see them as mythical. They've only heard stories about them, second-hand at best. They aren't quite 'real' to them until they've actually seen one. That doesn't mean there's some force oppressing them...
You are also talking about a species of highly intelligent and powerful beings that are
actively trying to hide. That is a far different thing from some people doing something and just not realizing it.
It seems to me that you just need to go ahead and accept the fact that you are artificially enforcing a
rule, or situation, upon your game world and it is OK. It is a tool by which you are telling a story. Just understand that it is by no means "realistic."