I think I understand your problem, but I may be misinterpreting so please correct me if I'm wrong. You've installed Personas 3 in one system, your "Personas system", and you're now accessing a different system, your "ECC system" and not seeing Personas. Is that right?
This arrangement of a single Personas installation supporting multiple backend systems was supported in Personas 2 but is not supported in Personas 3. Personas 3 must be directly installed in every system in which you wish to use it. In your case, you need to install it in your ECC system. Once installed, in exactly the same way you have installed it in your Personas system, it should just work - there is no configuration needed beyond activating a few SICF services as detailed in the installation guide.
Steve.