Part of it is the index percentage is tuned to the available shares so it didn't create an apocalyptic buying pressure. Plus he only got the Nasdaq to modify their rules which also tamped down the pop.

As for timing there's no universal answer, stock changes are usually announced a few trading days before it's effective so funds can use that time to perform their rebalances. I presume most of the funds that needed to start tracking SPCX started buying pretty early so they were properly balanced on the day it took effect it might have even been part of the initial pop though they could have also waited for the first tranches of insider shares that were released (I think there were some relatively early releases as part of the IPO?).