On Fi, your US stocks investing is almost real-time. When a Buy order is placed after a successful payment, your stocks get reserved as soon as the US market opens (if order is placed outside market hours) and get reserved instantly (if order is placed during market hours). The purchase is completed when the international transfer happens, however, the price one receives will be of the order fulfillment.
Note: All orders get implemented when the US market is open.
US Market timings: