We're talking minutes, and it has to be minutes, because the flight has to go, and people don't come in days before their flight, they come in an hour or an hour and a half before their flight. The whole process has to be handled in a matter of minutes. Most probably, if you put yourself in a situation where you're at the airport and there's a big lineup there, the person would probably be asked to step aside for a few minutes while papers are verified.
Then the airline agent would call the Transport Canada office 24-7 and give the Transport Canada officer information about the person, additional information like date of birth, which would be found on the ID card. The Transport Canada officer would in most cases be able to immediately say that this is not the person on the list, there is no issue with that person.
In the odd, remote cases where the person is in fact the person on the list, depending on the gravity of the situation, the information will be given back immediately by Transport Canada to the airline in the sense of an emergency direction, prohibiting the airline to board the passenger. At the same time, the airline will be asked to give a sheet or a paper to the passenger refused, telling the passenger he has the right to ask for reconsideration of his name being put on the list.