Hear me out on this: I don't like systems that just turn off the compressor and still run the fan. I think that is bad practice. These were very common over the last 3 decades or so. Today there is new tech. If I were to sign up for one of these plans, I'd rather they use a WiFi thermostat and just keep the whole system off.
Here's why:
In humid climates, de-humidification is just as important as cooling. During a cycle, when the compressor stops, most systems run the fan for about 30 seconds to capture the last of the cool in the coil. That's fine, but that's enough. If the fan continues to run after this, the latent moisture hanging on the coil evaporates and is injected back into the house. If the fan runs for even a longer time, the latent moisture collecting on the pan also evaporates and continues to raise the humidity in the house.
This doesn't matter as much in climates above the traditional Mason-Dixon line, or any climate in the West. For the Southeast where dew points frequently go above 70F, humidity control is paramount.
Need help visualizing it? Here's a picture of my 24 year old coil in action.