Pension funds don't tend to follow the S&P 500, much less automatically. They're sophisticated institutional investors like CalPERS [1] who dabble in everything from public stocks to private equity.
It's other retirement assets, e.g. 401(k)s and IRAs, that tend to follow the S&P 500. But again, with substantial variation.
S&P including these companies would have driven a lot of money towards them. But there was a lot of misinformation around the magnitude of that drive, as well as the breadth of whom it would affect.