All RF devices, whether they are zigbee or Z wave or something else, have to have some current going to the radio or they won’t hear the next “on” command for the network.
That said, most turn off enough that there won’t be any flickers provided you’re using compatible devices.
If the networked device is a dimmer that does not say it’s compatible with LEDs, it may produce exactly the behavior you are seeing. So it generally comes down to the specific model that you were using, not the brand.
I would go back to the user manual for the exact model that you have and see what compatibilities it lists. Then look for other models (whether it’s the same brand or a different one) which has a compatibility list that matches the devices you want to plug-in.
edited to update everything I wrote is still accurate, but may not be relevant since as @Navat604 points out, if this is a simple on/off module rather than a dimmer, normally it does kill all the power to the device that’s plugged into it. The radio still has power but that’s upstream from the device.