Rollover is a bookkeeping event, not a trading one. At the cut-off, every open position is pushed forward one value-date via tom-next, and the resulting debit or credit hits the account. Positions opened and closed within the same day never see it.
Around the cut-off, liquidity thins as banks change books between New York and Sydney. Spreads can widen for a few minutes and stops placed close to price are unusually exposed. Many traders avoid holding tight stops through it.
Example: a broker charges minus $9.40 per night to hold one lot of EUR/USD long. Held for 12 calendar days including one Wednesday, the cost is 14 charged days x $9.40 = $131.60, because the Wednesday roll counts triple.
Related: tom-next, triple-swap-wednesday, swap-rate