You may notice that your mini split fan continues to run for a while after the mini split is turned off - or continues to run after the room temperature has reached the set point.
This is normal operating behavior for a mini split.
Inverter driven mini splits are designed to run almost continually, slowly ramping up and down to modulate temperature, instead of turning on and off, like traditional HVAC systems. The slow ramping uses minimal energy, and is what makes mini splits so efficient.
Even though the set point may be reached and the outdoor unit isn't running, the fan on the indoor unit may continue to run. This is partly to help ensure that there is some air movement to help keep the room temperature more even.