I haven't found a full list of range activities, but there's a key comment in [this article][1]:  

> The Air Force currently requires several days to reconfigure its ranges between Atlas, Delta and Falcon missions. That turnaround time should be reduced with the introduction of auto-destruct mechanisms

So in the old situation, every user had its own self-destruct system that needed some unique equipment or configuration on the ground (because the system expects information in a unique format, for example). Because the self-destruct system is, well, destructive, they'd want to test the system after every reconfiguration to make sure it works and that no false destruct orders will be sent. That alone could take a few days. 

They'd also need to provide the Range Safety Officer (the person with the finger on the 'Destroy' button) with all the information they need for the decision, again unique information for every launch vehicle. 

In the new system, the flight termination rules are decided beforehand, and an automatic system on the rocket checks if the rules have been violated. That means you no longer need a ground-based system to receive and analyze telemetry, and translate the data for human consumption in real time. 

It turns out, that ground-based system was really [manpower-intensive][2]: 

>As the Brig. Gen. explained, “We have now gone completely autonomous with that system.  So with CRS-10 and all others with the AFTS, we’re able to reduce our operational footprint by 60% on day of launch."

> “So we came down 96 people that don’t have to be sitting on console.  And the cost to the customer is cut in half."

Those 96 people [were involved in][3]: 

> Comm, radar, transmitter, receiver, backup power generation, software, tracking cameras, console maintenance, etc  They would be located at the MOCC, JDMTA, Antigua, Cape command antenna site, camera sites, etc.


  [1]: http://21space.info/auto-destruct-system-seen-as-a-key-to-ramping-up-launch-tempos/
  [2]: https://www.nasaspaceflight.com/2017/03/air-force-reveals-48-launches-year-cape/
  [3]: http://forum.nasaspaceflight.com/index.php?topic=42567.msg1656548#msg1656548