Dual Mono is actually two unrelated mono instances.
The communication between them is done by the host using automation.
So if you moved a knob on one instance, and announced a parameter change, the host should pass that to the other.
There are no standard ways in the plugin API to talk to the other instance directly, although there are some hacky ways to do it if you really need to (send some custom message as a special parameter and decipher that on the other side, etc).
You can also talk to other instances via shared memory or file, but that’s also a bit hard, since the host isn’t telling the instance that you’re the “Dual Mono” of the other. As a plugin - you only know that you’re a mono instance, and hope the host handles it correctly.