0.24s is the standard differential between a hand-timed and an electronically timed performance. It is based on how fast the time keeper can react to seeing the smoke of the starting gun, and has nothing to do with the athlete’s reaction.
The formula 200m time = 2x100m time was deveoped when hand-timing was standard. If we assume that this formula is correct, we have to adjust electrically timed performances to hand-timed performances, then double them (for a 100m time) or half them (for a 200m time) and then adjust them back to an electrically timed performances: 2x(9.58-0.24)+0.24 = 18.92 (or simplified: 2x9.58-0.24 = 18.92).
BTW: Bolt’s reaction time for his 9.58 was 0.146.