Where did you set this? On the device or in a rule?
Also I think everything stated above is a little misleading. It mostly seems to be focusing on mains powers devices, not battery powered.
If you send a command to a zwave BATTERY (sleepy/sensor) device it does not work instantly. They will wake up on an interval, usually every 12 hours. The driver must wait for this wake up before it sends the command.
Zigbee battery devices somehow are always listening, I have no idea how it works. So yes you can send a command to a battery zigbee device any time and it usually responds right away. So your concern is valid.
Zwave is actually more efficient with batteries and because of this I found they usually have less / smaller batteries. My Zigbee devices last just as long if not longer but they are using two AAA batteries.
Final note, most battery devices are Sensors, they only send updates out and do not take commands (just configuration). For zwave if you have a battery device which needs to take actual commands, like a door lock, they are a special kind of battery device called FLIRS. They actually wake up every 60 seconds.
