What do you mean that the cancellations aren't instant? If they can outrun a bid to accept them that is instant as far as I'm concerned.
Your description of how companies are pricing orders is exactly what's happening. On a given exchange no cancel can outrun a bid to accept a resting order. In fact, you don't have any idea that the bid has arrived until after a trade has happened.
What is being described in the article is that a trader is viewing an aggregate of all exchanges as if they were one exchange (either due to ignorance, naivety, bad tools, or due to misrepresentation). The trader then takes out an entire price level at one exchange (none of those orders are cancelled) before trying to do the same thing at the other exchanges. The participants who just got filled at exchange A, then cancel their orders at exchange B. To the trader who was viewing multiple exchanges as a single entity this seemed like it happened all at once, but to the traders who were viewing the exchanges, correctly, as different entities there is a timeline that is observable and public (in fact nanex describes it).