Otherwise, again - if the PM gets paid the same whether or not the unit is vacant, will there be a sense of urgency (as, no doubt, the owner will have) to get the apartment rented?

But they have another similar one you can get if you move really quick, skip all DD and wire the money this afternoon... classic bait and switch topped with a sprinkle of manufactured urgency/ fear of missing out. 

Worst case, you have more than one potential tenant show up at the same time, which will create a sense of urgency in their minds.

The company didn't respond until Tuesday of the next week.It's all dependent on the individuals involved and the urgency to them to get your information verified.

You've got to show empathy and be able to explain how the process works so they understand the urgency of the situation.

You're absolutely right to be concerned about time urgency. 

The urgency should be on the sale, stay focused on your main goal; There used to be an old saying about when your up to your neck in alligators its' tough to think about your goal was to drain the swamp.

You have less urgency and more confidence in your voice.

There's an urgency (if not panic) for wholesalers without means to close other than using assignments and double closes.

However the nice thing about answering your call, besides the education, is that you can solve for the callers urgency factor faster.