One mantra of training is, “Do not over-promise.”
Many larger 9-1-1 centers separate the functions of call taker and dispatcher. While you speak to the call taker, they gather the information to pass it on to the dispatcher. Usually this is done using a Computer Aided Dispatch program.
So the person you are talking to may not be the person who is dispatching the police/fire service/ambulance. Until the call taker sees a unit assigned to the call and marked in responding status the call taker simply will not tell a caller that police are on the way. They might tell the call that “police will be there as soon as possible” or words to that effect.
Similarly, I would never promise how soon a responding unit will arrive. I might say “the ambulance is coming from their station on highway 12 next to the Wal-mart” but I would not say “they will be there in 3 minutes” It is rare, but responders are diverted to higher priority incidents or, worse I have had responders end up in a car wreck or have their vehicle break down on the way to a call.