Every single index fund is different. They all have publicly available methodology guides; you can read them to understand how it works and to model various scenarios.

This particular one, the CRSP total market - which Vanguard uses for VTI - has a “modern” methodology that is thought to be very good. Once every three months they re-rank the entire market and assign weights based on the market as of a particular point in time. Then, a randomly-chosen number of days later, the fund (Vanguard) begins a weeklong reconstitution process in which they buy and sell stocks to reflect the new weights. It is intentionally a weeklong process so that the market is setting prices and not Vanguard with the size of their orders.

The lockup expiry happens, the market reacts, the market is re-weighted, the index reconstitutes. In that order. The price of the stock has to survive the increased float to force the index fund to buy lots more shares.