I will try to make it less confusing but I am not sure I understand exactly what you are asking. I don't work for LACoFD so I don't know if all my info is correct.
A 9-1-1 comes into the dispatch center where a call taker answers it and asks pertinent questions. The call information is then sent to the blue 8 dispatcher which dispatches calls countywide. The dispatcher lines up who is being sent to the call and sends the call info to MDTs, station printers and the station alerting system. The dispatcher waits 5-7 seconds and then dispatches the call with the high-low tone. If there are multiple calls backed up, you will hear an abreviated dispatch (structure 59......rescue 33.... Traffic collision 76). If there are numerous calls backed up then there is no voice dispatch. There is no other traffic allowed on blue .
The call info is then sent to a tactical radio operator (TRO) which is basically a regional dispatcher that only talks with units within that region of the county. If there is a unit not in quarters or already on a call, the TRO will announce the call over the radio (rescue 36, squad 116). This means there is a medical emergency in station 36's area and squad 116 is assigned to the call. If engine 36 is not in quarters, the engine will hear they have a response. If squad 116 is responding, this means squad 36 is not available for a response in their area. This also means that squad 36 would hear it and can go available if possible for the new call. Announcing the call also allows other units to hear it and possibly respond if they are closer then the original unit.
The UHF blue channels are for dispatch and unit to dispatch communications. The VHF channels are for on scene fireground communications.
Here is a link to the response matrix.
Los Angeles County Fire Department - Special Ops - 911 Dispatch - Response Matrices