Unlikely as it may seem, there must be several versions/revisions of Theodore R. Cogswell's The Wall Around the World.
The one I read ends with Porgie succeeding in overclocking a broomstick so that he is able to reach the top of the Wall, after his teacher Mr. Wickens punished him for his dream of doing so by domesticating some eagles; then, the Black Man arrives and gets Porgie, revealing himself to be none other than Mr. Wickens with a flying harness from Outside. In his youth, Mr. Wickens too succeeded in going Outside - by going up a mountain and capturing himself some eagles. Now he'll get Porgie outside to have him educated before going back Inside.
A slightly different ending is here in this answer. Here, the explanation is the same, but Porgie appears to be brought back immediately. To be fair, this might also be nothing more than a slight recollection error.
A third version I have already heard mentioned [in Cambridge, UK, around 1990-1995], but haven't been able to find, is yours. There, Porgie arrives Outside, and discovers that the same "rules" apply Outside - they do not know there's an Inside, they think they are those Inside, going Outside is forbidden etc. .
To confirm, there's another detail you did not mention that I heard: Outside, magic sometimes works less reliably than Porgie is used to, so much that be believes he's losing his powers (this is similar to the Hell's Gate universe). Upon discovering that his magic never fails him when he's alone, Porgie works it out that it all depends on belief - he knows that magic works, and the more he shows it to be working to others, the less people disbelieve him, and the more it works. That's the missing ingredient that allows at last the Wall to be torn down.
If this matches too, then apparently either Cogswell or someone else wrote a sequel or a "reboot" of the novelette, expanding on the end. I am reasonably convinced that it must have appeared on Proceedings of the Institute for Twenty-First Century Studies.