Are you referring how it does a `brew upgrade` when doing a `brew install`? It should tell you how to disable that whenever it happens:
> Adjust how often this is run with `$HOMEBREW_AUTO_UPDATE_SECS` or disable with
> `$HOMEBREW_NO_AUTO_UPDATE=1`. Hide these hints with `$HOMEBREW_NO_ENV_HINTS=1` (see `man brew`).