When our air conditioning is running the compressor will kick off but the fan continues to run until we manually turn the Raeburn 5000 thermostat to the off position. This am while the thermostat was in the off position the fan came on and ran for about 5 minutes. I also noticed, and it may have bee coincidental, but when I turned the thermostat to off when the fan wouldn't cycle off itself, on of out smoke detectors went off briefly.

My husband in an HVAC tech (heating, ventilation, air conditioning) and has to fix things like this all the time. Call whoever services your unit and report this so they can either fix it or explain to you why it does this if it's supposed to be doing that. As an addendum, the smoke detector shouldn't be going off, so it's probably something that should be fixed.