I think "Subscriber" would imply trying to contact the person responsible for the alarm system. On a commercial account that would mean calling down the call-list until someone is reached. On a residential it would mean just calling the premises and any other wireless numbers the owner may have, but not the others on the call list.
Depending on the time-of-day, they may want the premises tried or not, if the account gets setup properly then the system knows what to do at what times and prompts the Operators appropriately.
It really comes down to "what did you TELL them to do in that scenario" since all monitoring centers tend to do things differently based on their flow of signals and how automated things are. If somethings becomes too cumbersome for their operators, they either automate it (sometimes too much), or stop doing it (like calling down call lists because it is time consuming). Not that they Won't do it, they just stop doing it as SOP and instead only when requested specifically to do so.
Review the default actions the monitoring center will take under each circumstance and make sure it is taylored to the way you want it done for all accounts in general, then taylor the individual accounts as necessary from there. A good Monitoring Center can handle every signal any way you want, as long as it is communicated to them properly and in advance.