In my country, generally for apartments, when a fire alarm sounded, only the affected floor and the immediate above and lower floor will be sounded and beacons will flash but all elevators will be homing. The whole building will be in alarm when the evacuation button is pushed or if there no response from the control room when the prerequisites time has passed, usually 5 mins.

Only then, the rest of the building will be instructed (only when needed) to evacuate in phase starting with the level above the affected floor.

However, not all building practice this kind of system, especially old building. Most of new building started to have this kind of egress method. Some buildings have refuge area designed in some floors like how a hospitals are designed.

Other kind of commercial building has different strategy as per approved by the fire authority.