St. Clares recently renamed all their unit callsigns. Their BLS go by Ambulance # and their ALS go by MIC ##. When a Clares unit gets assigned to a call for a town that is not dispatched by their own communications center they sign on with the local dispatch center (which happens to be Morris County Comm Center a lot). So you will hear a Clares unit give updates on their own DMR system as well as the local dispatch center for the town they are responding into.
As far as Atlantic units go, for the towns they are primary for, their BLS get dispatched by the local comm center. So for example Rockaway Boro, EMS 15 gets dispatched on EMS Resp 2 by the Morris County Comm Center. I have heard a few other Atlantic BLS units get dispatched this way for other towns. Sometimes I hear them give updates on their DMR system as well as the local dispatch, sometimes not.
Long story short, they probably get dispatched via the same comm center that does police and fire for Bernards. Find out who that is and find what the EMS response channel is and you will probably hear them. Not much information gets transmitted over the Spectrum DMR system. Also keep in mind every unit has a Toughbook in it that gives the unit information on the call. This keeps information transmitted over the air to a minimum unless the Toughbook is not working.
Sorry if this is redundant information or not helpful to you but maybe it will help someone out.