The small cone is connected to the larger one. The coax center cable is terminated into the small cone and the coax shield into the larger outer cone.
The screenshots are from this video https://www.youtube.com/watch?v=Pu-o4u3VgR0
Another video from a different manufacturer - https://www.youtube.com/watch?v=y8ky1t3IfLE
They claim wideband coverage from 700 Mhz to 2.5ghz, but I suspect they simply do not do anything.
I have one of them and I think these are the reason my setup is failing.
Could they even work?
I couldn't find any teardown of any dome antenna from any of the big companies except this one - https://www.youtube.com/watch?v=7EB4wqawBv4 - but this seems to be a completely different design.