How did they talk to MacLaren for so long after stopping him from falling?

McLaren “took so long to die” because he technically didn’t die. The director chooses at any moment who will be overwritten. Perfect example: in Traveler episode “Aleksander” agent McLaren is ordered to kill Aleksander, but then decided not to. In theory, Aleksander should be dead at 15:00, but wasn’t. This is because death is prevented, and the director had the choice to kill Aleksander like the director did to sandstorm, or let him live.
This is why “don’t take a life, don’t save a life” is a rule. The director can calculate the future based on the decision it makes, but it can’t factor in human decisions.

Basically if you move the subject out of death's reach, they will still live until either natural law or the director takes over.

Catija assumed right.
In the meantime Season3 was released and gave us some more insight.
At one point in Season3, McLaren (Traveler 3468) mentions that his host would've bled out in the elevator shaft, pointing out that what Director did to his host was in a way merciful, because McLaren's death would not have been instant.
This explains why it took some time for McLaren to get overwritten.

The logical explanation for this is that he fell but wasn't killed immediately from the fall.

While nearly every fall from over 100 feet (~30 meters) is fatal, that doesn't mean that it's instantly fatal. In fact, there are documented cases of people falling hundreds of feet and surviving. Here's an abstract about a woman who survived a 300 foot fall while rock climbing.

A more recent study on 287 vertical fall victims revealed that falls from height of 8 stories (i.e. around 90-100 feet) and higher, are associated with a 100% mortality. Thus, a vertical falling height of more than 100 feet is generally considered to constitute a "non-survivable" injury.

The present case report describes the rare survival of a 28-year old rock climber who survived a free fall from 300 feet onto a solid rock surface. This report emphasizes the crucial relevance of body positioning at the time of impact, and the importance of standardized institutional "damage control" management protocols for survival.

So, this two to three minutes of exposition time could be reasonably explained as being the time between his fall and his actual time of death.