GS mini takes tailwind gusts into account as well as headwind gusts, (within certain limits).
GS Mini reacts to the instantaneous head or tailwind gusts, and is automatically smoothly reduced so as not to command high speed changes in the flare.
Pulling selected speed stops GS Mini from working, and that could reduce the aircraft energy below a safe level. As Fursty Ferret says; GS Mini should be programmed with the Tower Wind before commencing the approach; not overridden on short finals.
Old conventional systems have to fly fixed IAS, because any change in IAS affects the pitch trim, so this would cause the aircraft to deviate. Airbus FBW auto-trims, (and also designs-out the pitch/power couple), so the designers could look again at the situation and did not need to stay with fixed IAS.
GS Mini takes the reported Tower Wind into account and computes a minimum groundspeed - and therefore a minimum energy - instead of a fixed IAS. In practice therefore, it reacts the opposite way round from the old conventional constant IAS systems - GS Mini will call for increased thrust during a headwind gust, and vice versa, (within certain limits). It does this to preserve energy, so if you cancel or override an IAS or thrust increase commanded by GS Mini, you are reducing the aircraft energy, which could leave you in a bad place.