Hello and welcome to JustAnswer!
If the system was completely discharged then you're correct, there would be no cooling whatsoever. There had to have been enough left in the system to allow the compressor to run. With the way that airflow is set up in many modern heater boxes the air flowing over one side of the a/c evaporator goes to one side of the vehicle only rather than having a common plenum, so when a/c charge gets low and partially cools the evaporator it will cause a temperature difference between sides.
I'm wondering if the noise you heard was refrigerant escaping the pressure relief valve on the compressor. If pressure went extremely high it would have vented. This could have been from something like an expansion valve that isn't opening or possibly the cooling fan not working, or it could just be the valve itself.
If it does start to warm up again then they'll be able to use a UV light to look for traces of the dye that they injected.