Mini Splits operate differently than central heating and cooling units; central heating and cooling units turn off the fan when room temperature is met, however because ductless mini splits are room air conditioners they do not have but one outlet for the air to go out and into so they must keep the fan running to ensure temperature is not different from one end of the room to the other. Therefore, it is normal and proper operation for the fan to run in the off-cycle of the compressor however these fans are extremely low energy use and require less energy to stay running than a typical fan does to start on and off, also DuctlessAire mini split systems are designed to be almost noiseless so you should not even be able to hear the system operating.
A central heating and air unit may have, up to, a 3-5 degree differential before it turns the unit back on. This could also lead to the unit short cycling. The constant on and off of the unit is somewhat like turning your car off and back on at every stop light which leads to inefficiency and wearing out of parts.
Our DuctlessAire unit indoor fan runs continuously so that the fan slowly moves air throughout the conditioned space, monitoring the temperature of the air returning to the fan coil. This action provides accurate temperature control and allows the system to quickly react to changes in room temperature which leads to a more comfortable environment. This leads to cleaner air as the filters are utilized more so be sure to wash them every other month.