Security question about processes interactions between GZ and NGZ

In another post, Running Firefox from a zone, I've got one security doubt.
If when attempting to run Firefox from a remote NGZ, by default it attemps to "attach" to the "global" firefox process in the GZ, what about the security isolation between GZ and NGZs?
Note: It seems the attempt succeeds as the "Error: no display specified" is displayed (even it that's not the intended behavior).

Thanks in advance.