There is no single correct roll date. Index futures conventionally roll on the Thursday a week before expiry; crude rolls several days before first-notice-day; index funds follow published schedules. What matters in practice is where volume and open-interest are, because that is where your fills will be good.
Rolling late costs you liquidity; rolling early costs you a few days of thinner markets in the new month. Most active traders watch both months' volume and switch on the day the new month takes the lead.
Example: in the week before ES expiry, September volume falls from 1.5 million to 400,000 contracts while December rises past it. That crossover day is the practical roll date.
Related: roll, continuous-contract, front-month, first-notice-day