How does the Airbus ECAM / ND transfer work?
All this depends on the A320 generation. On early models all computations are done by the SDACs and the DMCs, and the switching corresponds to data switching in the DMCs, so the screen will display what it receives.

On later models all screens receive all data and on request they can display what you ask when you do the ECAM/ND switching.

In fact in latest models of A320 the displays switching possibilities are voluntarily limited just for conformity with earliest A320’s