The typical home setup guide tells you to disable DHCP on your repeater and delegate to the original box. I was told to do that when I set up something similar due to living in a U-shaped apartment with no nice central position for the router.
But if the original network is unavailable - perhaps the SSID has changed for example - you need to be able to get to the repeater's configuration page somehow. And the user can't google their problems or download any configuration tools while their connection is down, so you'd better make it simple. So many devices like this will be transparent under normal operation, but if there's a network problem will start their own DHCP server.