It seems like what you are asking about is your sons secure position on the team. As in - the Caltech coach has not promised my son a spot on the team or a certain amount of playing time. Generally D3 coaches don’t promise that. What they promise is help with admissions, which your son received. You can probably safely assume that your son will make the team regardless of coach turnover. It does happen that coach turnover changes a team but it’s not generally that the recruits don’t make the team, it’s more likely to shake out in playing time.
You are chasing something that doesn’t exist as far as I’m aware of. If your son has been admitted and you can afford the school, consider yourself done.