The acharonim (see the Mateh Efraim and Aruch Hashulchan at the end of Siman 624) bring down a minhag to get up early to daven the day after Yom Kippur so the Satan will not be able to complain.
Somehow this has turned into a minhag to start davening 5 minutes earlier. The 6:30 minyan starts at 6:25 the 7:00 minyan starts at 6:55 and even the 8:00 minyan starts at 7:55.
IMHO I don't see how this is mekayem the minhag at all. There is no way that going 5 minutes early to an 8:00 minyan is called משכימים. This is just another instance where the spirit of the minhag is completely ignored for a doubtful mechanical kiyum.