Can someone elaborate how response to hostage threat works in US? Here in India, depending upon the situation, one of the security forces(police, paramilitary,

Can someone elaborate how response to hostage threat works in US? Here in India, depending upon the situation, one of the security forces(police, paramilitary, Army, special forces, swat, etc), or combination of them, respond, and first cordon off the area. Then, the alleged criminals/terrorists are asked through loudspeakers to surrender. If they do, good. If they don't, and start shooting on security forces/civilians, then they kill them. How does it work in US? Was this guy not asked to surrender?