You'll recognize soon after playing a few games which events will cause a conflict. (Shots fired, send backup!)
Some examples are drug dealers, home invasions, sometimes fights
When your police arrive at such events, there is a short delay before the "send backup" notice happens.
To get the achievement, you need 3 police units on scene before the backup request is made.
Easiest way is to send police near the event, then send them all in at once.