My experience with furnace blowers has shown that if you are using the fan as a circulator (fan ON) and the the unit receives a call for either heating or cooling it will first stop the fan and the initiate either the heating or cooling sequence. If cooling, the fan may only stop for a couple seconds. For [gas] heating, the fan will remain off a bit longer until the main heat exchanger gets up to temp.
There is also an “anti-short cycle” timer that prevents an AC compressor from restarting too soon after the previous run cycle. Example: unit is running in cooling mode when the space reaches set point. Compressor stops, fan continues to run for a short time to use up the “residual cold” in the coil and then stops. Thermostat calls for another cooling cycle before the timer had expired. Even though the thermostat is calling for cooling, the compressor and fan will not start until the anti- short cycle timer has expired and allows the cycle to begin. This can be exaggerated by “zoned” systems where the various zones just happen to be “out of sync” with each other.
I’m guessing that the ecobee only reports what it is commanding the HVAC system to do, but has no actual feedback to know if/when that command gets executed.