Can I use a supplementary lens on iPhone 13 camera?

In the past, with iPhones that had only one camera (e.g. the iPhone 7), it was possible to add a supplementary lens, for example for telephoto or ultra-wide angle. The system was simple: a third party lens kit (sometimes approved by Apple and sold in the Apple stores) consisted of a clip and some lenses. The clip simply fixed the supplementary lens to the body of the iPhone in such a way as to allow the extra lens to 'see' through the iPhone's camera. The quality of the resulting image, especially at the edges, was imperfect, but nevertheless the system could produce very useful results, for example for bird photography.

I wanted to do the same thing for the iPhone 13 Pro, which has three cameras. I bought a kit, which works exactly as described above, but I can't get it to work. What I think is happening is that the phone's camera software interprets the clipped-on lens to be some kind of obstruction of the camera chosen, and simply switches to one of the other two cameras, so the supplementary lens isn't being used. I think this happens with the telephoto in particular - but it could of course just be that I'm too clumsy while attaching the lens.

Does anyone know whether my idea is correct, and if so, is there a workaround? I'm still experimenting, but it would be good to know more about how the 3-camera system actually works.