At this point the beer is still evolving CO2 so no air enters the cask. The soft spile serves to ensure that the beer does not become overcarbonated. Once CO2 evolution has ceased air could enter the cask so at this point the soft spile is replaced with the hard spile. The whole system serves to ensure that the beer achieves perfect condition. There is no particular advantage to one time point over another.
Some cellar keepers leave the tap partly open whilst driving it through the keystone.
Ostensibly this ensures that air is not driven into the cask, but it is questionable whether this is of benefit. Occassionally it may be necessary to replace the tap on a full cask, usually the cause is a leaking tap. This isn't the disaster it may appear. First insert the hard spile into the cask, this produces an air lock so that little beer will escape the cask. Gently rock the tap whilst holding it into the keystone .