When you hear "Tone then "Rescue 120's area, Squad 119" what they are doing is called a "pre-alert" on the geographical command frequency for that region. That gives those units who are monitoring the radio channel a heads up that there is a call in that area. The Squad is a utility truck with 2 paramedics but no transport capability. Medical aid calls in LA County region (unincorporated areas and contract cities) have an engine/truck company assigned, as well as a squad, and then a private ambulance which is assigned to that area by the LA County Board of Supervisors. The private ambulance is not dispatched on the fire frequency.
What you are not hearing, unless you are listening to BLUE 8 Frequency 470.5375, is the entire dispatch or the "real" dispatch channel. There is so much radio traffic, that most units don't listen to that frequency, they just listen to their area command channel.
The reason a pre-alert is done on the geographical/regional command frequency is that you may have units on scene of a call, and a second call comes in for their area. By broadcasting it on their geographical/regional command channel, it gives them the info and if they can leave their current call, or become available, for instance, at the hospital after offloading, they can tell dispatch and take the call.
Also, LACOFD does not use GPS/AVL locators, so their dispatchers don't know exactly where they are, and it gives the units in the field the opportunity to take a call they may be closer to,or tell dispatch they are too far away, and send the next closest unit.
This feed:
Los Angeles County Fire - Blue 8 Live Scanner Audio Feed will allow you to hear all dispatches countywide
This feed
Los Angeles County Fire - Blue 6 Live Scanner Audio Feed allows you to hear the San Gabriel Valley geographical command channel.
Finally, units are not allowed to talk on the main dispatch channel, Blue 8, to the dispatcher. They have to use their command channel so they don't interrupt dispatches that are being broadcast.