The Nasdaq market system doesn't have a native stop facility so all stops for any broker must be kept on internal servers.
Perhaps the lag you have seen is from IB's feature where they wait to send the order until 2 trades at the bid/ask take place? If so, they recently added an alternate scheme where one can elect to have the stop triggered based on a single price on the tape. I actually prefer the first method myself.
The NYSE does have a native stop facility but IB doesn't use it so as to not tip the specialist's hand, since he would then be able to see the stop order in his book.